From d1b10fdd1002763fbd6ecbe4659013abc4286768 Mon Sep 17 00:00:00 2001
From: jcrayb <jcrb7800@gmail.com>
Date: Sat, 18 Jan 2025 11:11:27 -0600
Subject: [PATCH] fixed links in dyn and sta

---
 src/pages/dyn/particle_kinematics.astro | 30 ++++++------
 src/pages/dyn/particle_kinetics.astro   |  8 ++--
 src/pages/dyn/vector_calculus.astro     | 18 +++----
 src/pages/dyn/vectors.astro             | 62 ++++++++++++-------------
 src/pages/sta/vectors_scalars.astro     | 14 +++---
 5 files changed, 66 insertions(+), 66 deletions(-)

diff --git a/src/pages/dyn/particle_kinematics.astro b/src/pages/dyn/particle_kinematics.astro
index 0f5b81af..46ba3dc6 100644
--- a/src/pages/dyn/particle_kinematics.astro
+++ b/src/pages/dyn/particle_kinematics.astro
@@ -278,7 +278,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
       </table>
       <p class="figureCaption mt-2">
         Velocity and acceleration in the polar basis. Compare to
-        Figure <a href="#rkv-fa">#rkv-fa</a>. Observe that
+        Figure <a href="#rkv-fa-c">#rkv-fa</a>. Observe that
         <InlineEquation equation="\\hat{e}_r,\\hat{e}_\\theta" /> are not related to the path
         (not tangent, not in the direction of movement), but
         rather are defined only by the position vector. Note also
@@ -456,12 +456,12 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <DisplayEquation title="Derivative of general vectors." id="rkr-ed" background="True" derivation="True" equation="\\begin{aligned}\\dot{\\vec{a}} = \\underbrace{\\dot{a}\\hat{a}}_{\\operatorname{Proj}(\\dot{\\vec{a}}, \\vec{a})} +\\underbrace{\\vec{\\omega} \\times\\vec{a}}_{\\operatorname{Comp}(\\dot{\\vec{a}}, \\vec{a})}\\end{aligned}">
         <p>
             Using the same approach as <a
-            href="rvc.html#rvc-em">#rvc-em</a> we write <InlineEquation equation="\\vec{a} =a\\hat{a}" /> and differentiate this and use <a
+            href="/dyn/vectors#rvc-em2">#rvc-em</a> we write <InlineEquation equation="\\vec{a} =a\\hat{a}" /> and differentiate this and use <a
             href="#rkr-ew">rkr-ew</a> to find:
 
             <DisplayEquation equation="\\begin{aligned}\\dot{\\vec{a}} &amp;= \\frac{d}{dt} \\big( a \\hat{a} \\big) \\\\&amp;= \\dot{a} \\hat{a} + a \\dot{\\hat{a}} \\\\&amp;= \\dot{a} \\hat{a} + a (\\vec\\omega \\times \\hat{a}) \\\\&amp;= \\dot{a} \\hat{a} + \\vec\\omega \\times (a \\hat{a}) \\\\&amp;= \\dot{a} \\hat{a} + \\vec\\omega \\times \\vec{a}.\\end{aligned}" />
 
-            Comparing this to <a href="rvc.html#rvc-em">#rvc-em</a>
+            Comparing this to <a href="/dyn/vectors#rvc-em2">#rvc-em</a>
             shows that the two components are the projection and the
             complementary projection, respectively.
           </p>
@@ -617,7 +617,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         <p>
             Using <a href="#rkr-el">#rkr-el</a> and the scalar
             triple product formula <a
-            href="rvi.html#rvi-es">#rvi-es</a> gives:
+            href="https://en.wikipedia.org/wiki/Triple_product">#rvi-es</a> gives:
 
             <DisplayEquation equation="\\begin{aligned}\\vec{a} \\cdot \\dot{\\vec{a}}&amp;= \\vec{a} \\cdot \\big( \\vec{\\omega} \\times \\vec{a} \\big) \\\\&amp;= \\vec{\\omega} \\cdot \\big( \\vec{a} \\times \\vec{a} \\big) \\\\&amp;= 0.\\end{aligned}" /> 
           </p>
@@ -627,7 +627,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         <p>
             We first consider the dot product <InlineEquation equation="\\vec{a} \\cdot \\vec{b}" /> and show that this is not changing with
             time. We do this by using the scalar triple product
-            formula <a href="rvi.html#rvi-es">#rvi-es</a> to find:
+            formula <a href="https://en.wikipedia.org/wiki/Triple_product" target="_blank">#rvi-es</a> to find:
 
             <DisplayEquation equation="\\begin{aligned}\\frac{d}{dt} \\big( \\vec{a} \\cdot \\vec{b} \\big)&amp;= \\dot{\\vec{a}} \\cdot \\vec{b} + \\vec{a} \\cdot \\dot{\\vec{b}} \\\\&amp;= (\\vec{\\omega} \\times \\vec{a}) \\cdot \\vec{b} + \\vec{a} \\cdot (\\vec{\\omega} \\times \\vec{b}) \\\\&amp;= \\vec{b} \\cdot (\\vec{\\omega} \\times \\vec{a}) + \\vec{b} \\cdot (\\vec{a} \\times \\vec{\\omega}) \\\\&amp;= \\vec{b} \\cdot (\\vec{\\omega} \\times \\vec{a}) - \\vec{b} \\cdot (\\vec{\\omega} \\times \\vec{a}) \\\\&amp;= 0.\\end{aligned}" />
 
@@ -722,7 +722,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         These equations are definitions of the basis vectors, so
         the only thing to derive is the alternative formula for
         <InlineEquation equation="\\hat{e}_n" />. Using the definition of <InlineEquation equation="\\hat{e}_t" /> above
-        and <a href="rvc.html#rvc-eu">#rvc-eu</a>, we see that
+        and <a href="/dyn/vectors#rvc-eu">#rvc-eu</a>, we see that
 
         <DisplayEquation equation="\\dot{\\hat{e}}_t = \\dot{\\hat{v}}        = \\frac{1}{v} \\operatorname{Comp}(\\dot{\\vec{v}}, \\vec{v})        = \\frac{1}{v} \\operatorname{Comp}(\\vec{a}, \\vec{v})." />
 
@@ -824,7 +824,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
 
       Now the basis vector derivatives are given by the cross
       product by <InlineEquation equation="\\vec{\\omega}" /> from <a
-      href="rkr.html#rkr-ew">#rkr-ew</a>, so we can evaluate
+      href="#rkr-ew">#rkr-ew</a>, so we can evaluate
       the expressions <a href="#rkt-ek">#rkt-ek</a> for
       curvature and torsion to give:
 
@@ -857,7 +857,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <p>
       We can use the expression <a href="#rkt-ew">#rkt-ew</a>
       for <InlineEquation equation="\\vec{\\omega}" /> together with <a
-      href="rkr.html#rkr-ew">#rkr-ew</a> to find the basis
+      href="#rkr-ew">#rkr-ew</a> to find the basis
       vector derivatives:
 
       <DisplayEquation equation="\\begin{aligned}\\dot{\\hat{e}}_t &amp;= \\vec{\\omega} \\times \\hat{e}_t= (v\\tau \\,\\hat{e}_t + v \\kappa \\,\\hat{e}_b) \\times \\hat{e}_t= v \\kappa \\,\\hat{e}_n \\\\\\dot{\\hat{e}}_n &amp;= \\vec{\\omega} \\times \\hat{e}_n= (v\\tau \\,\\hat{e}_t + v \\kappa \\,\\hat{e}_b) \\times \\hat{e}_n= - v \\kappa \\,\\hat{e}_t + v \\tau \\,\\hat{e}_b \\\\\\dot{\\hat{e}}_b &amp;= \\vec{\\omega} \\times \\hat{e}_b= (v\\tau \\,\\hat{e}_t + v \\kappa \\,\\hat{e}_b) \\times \\hat{e}_b= -v \\tau \\,\\hat{e}_n.\\end{aligned}" />
@@ -945,7 +945,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         direction of <InlineEquation equation="\\vec{v}" />, that
         <InlineEquation equation="\\operatorname{Comp}(\\vec{a},\\vec{v})" /> does not depend
         on the magnitude of <InlineEquation equation="\\vec{v}" />, and equation <a
-        href="rvv.html#rvv-em">#rvv-em</a> for the magnitude of
+        href="#rvv-em">#rvv-em</a> for the magnitude of
         the complementary projection.
       </p>
     </DisplayEquation>
@@ -1086,7 +1086,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   <InlineEquation equation="\\hat{e}_b" />. At the current instant when the particles
   are at the same position, this means that <InlineEquation equation="\\hat{e}_r =  -\\hat{e}_n" /> and <InlineEquation equation="\\hat{e}_\\theta = \\hat{e}_t" />. Using the
   circular motion expressions <a
-  href="rke.html#rke-ep">#rke-ec</a> we have that the
+  href="https://en.wikipedia.org/wiki/Circular_motion" target="_blank">#rke-ec</a> we have that the
   velocity of \(Q\) is:
 
   <DisplayEquation equation="\\begin{aligned}  \\vec{v}_Q &amp;= v_Q \\,\\hat{e}_\\theta \\\\  &amp;= \\dot{s}_Q \\,\\hat{e}_\\theta \\\\  &amp;= \\dot{s}_P \\,\\hat{e}_t = \\vec{v}_P. \\\\  \\end{aligned}" />
@@ -1179,7 +1179,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         <DisplayEquation equation="\\begin{aligned}\\|\\vec{r}'' \\times \\vec{r}'\\| &amp;= \\|\\vec{a} \\times \\vec{v}\\| \\\\&amp;= a v \\sin\\theta \\\\&amp;= \\frac{v^3}{\\rho},\\end{aligned}" />
 
         where we used the cross product length formula <a
-        href="rvv.html#rvv-el">#rvv-el</a> and equation <a
+        href="/dyn/vector_calculus#rvv-el">#rvv-el</a> and equation <a
         href="#rkt-er">#rkt-er</a> for the radius of curvature
         <InlineEquation equation="\\rho" />. By definition <a href="#rkt-ek">#rkt-ek</a> the
         curvature is <InlineEquation equation="\\kappa = 1/\\rho" />, so
@@ -1218,12 +1218,12 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <DisplayEquation title="Curvature of an explicitly defined function \\(y = f(x).\\)" id="rkt-e3" background="True" derivation="True" equation="\\kappa = \\frac{|y''(x)|}{(1 + y'(x)^2)^{3/2}}">
       <p>
         Use equation <a
-        href="rkt.html#rkt-e2">#rkt‑e2</a> and parametrize the curve using \(x\) as the parametrization variable. Namely:
+        href="#rkt-e2">#rkt‑e2</a> and parametrize the curve using \(x\) as the parametrization variable. Namely:
 
         <DisplayEquation equation="\\begin{aligned}x = u, \\quad \\quad y = y(u) = y(x)\\end{aligned}" />
 
         This yields a very elegant expression, as <InlineEquation equation="x'(u) = 1" /> and <InlineEquation equation="x''(u) = 0" />, which lets us arrive at the desired expression <a
-        href="rkt.html#rkt-e3">#rkt‑e3</a>.
+        href="#rkt-e3">#rkt‑e3</a>.
       </p>
     </DisplayEquation>
 </SubSubSection>
@@ -1595,8 +1595,8 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <CalloutContainer slot="cards">
       <CalloutCard title="Reference material">
         <ul>
-          <li><a href="rkv.html">Position, velocity, and acceleration</a></li>
-          <li><a href="rkt.html">Tangential/normal coordinates</a></li>
+          <li><a href="#velocity_acceleration_vectors">Position, velocity, and acceleration</a></li>
+          <li><a href="#tangential_normal_basis">Tangential/normal coordinates</a></li>
         </ul>
       </CalloutCard>
     </CalloutContainer>
diff --git a/src/pages/dyn/particle_kinetics.astro b/src/pages/dyn/particle_kinetics.astro
index 2bafeeb2..60ef2cbd 100644
--- a/src/pages/dyn/particle_kinetics.astro
+++ b/src/pages/dyn/particle_kinetics.astro
@@ -185,7 +185,7 @@ import DisplayTable from "../../components/DisplayTable.astro"
               <p>
                 <strong>2. Kinematics:</strong> Using the polar
                 basis acceleration equation <a
-                href="rkv.html#rkv-ep">#rkv-ep</a> gives:
+                href="/dyn/particle_kinematics#rkv-ep">#rkv-ep</a> gives:
                 <DisplayEquation equation="\\begin{aligned} \\vec{a} &amp;= (\\ddot{r} - r\\dot\\theta^2) \\,\\hat{e}_r + (r\\ddot\\theta + 2\\dot{r}\\dot\\theta) \\,\\hat{e}_\\theta \\\\ &amp;= -\\ell \\dot\\theta^2 \\,\\hat{e}_r + \\ell\\ddot\\theta \\,\\hat{e}_\\theta. \\end{aligned}" />
               </p>
               <p>
@@ -446,8 +446,8 @@ import DisplayTable from "../../components/DisplayTable.astro"
         <CalloutContainer slot="cards">
             <CalloutCard title="Required material">
                 <ul>
-                    <li><a href="rep.html">Kinetics of point masses</a></li>
-                    <li><a href="reg.html">Kinetics of rigid bodies</a></li>
+                    <li>Kinetics of point masses</li>
+                    <li><a href="/dyn/rigid_body_kinetics">Kinetics of rigid bodies</a></li>
                   </ul>
             </CalloutCard>
             <CalloutCard title="Extras!">
@@ -611,7 +611,7 @@ import DisplayTable from "../../components/DisplayTable.astro"
         class="seq-toggle:avb-fp-c:fbd" onclick="avb_fp_c.stepSequence('fbd')">free body diagram</button>
         is visible. Now increase the speed of the bus to produce a
         centripetal acceleration. <a
-        href="rkn.html#rkn-en">Newton's law</a> implies that there
+        href="/sta/introduction#rkn-en">Newton's law</a> implies that there
         must be a centripetal friction force producing this
         acceleration. As the speed increases, we will eventually
         reach a point when the friction force required is too large
diff --git a/src/pages/dyn/vector_calculus.astro b/src/pages/dyn/vector_calculus.astro
index cf4ab238..f67a8d99 100644
--- a/src/pages/dyn/vector_calculus.astro
+++ b/src/pages/dyn/vector_calculus.astro
@@ -63,7 +63,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         product</em> or <em>scalar product</em>) is defined by
       </p>
 
-    <DisplayEquation equation="\\vec{a} \\cdot \\vec{b}= a_1 b_1 + a_2 b_2 + a_3 b_3" title="Dot product from components." background="True"/>
+    <DisplayEquation equation="\\vec{a} \\cdot \\vec{b}= a_1 b_1 + a_2 b_2 + a_3 b_3" title="Dot product from components." background="True" id="rvv-es"/>
 
     <p>
         An alternative expression for the dot product can be
@@ -177,7 +177,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   <DisplayEquation id="rvi-ed" title="Dot product symmetry." equation="\\vec{a} \\cdot \\vec{b} = \\vec{b} \\cdot \\vec{a}" background="true" derivation="true">
     <p>
       Using the coordinate expression <a
-      href="rvv.html#rvv-es">#rvv-es</a> gives:
+      href="#rvv-es">#rvv-es</a> gives:
 
       <DisplayEquation equation="      \\vec{a} \\cdot \\vec{b}      = a_1 b_1 + a_2 b_2 + a_3 b_3      = b_1 a_1 + b_2 a_2 + b_3 a_3      = \\vec{b} \\cdot \\vec{a}." />
     </p>
@@ -186,7 +186,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   <DisplayEquation id="rvi-eg" title="Dot product vector length." equation="\\vec{a} \\cdot \\vec{a} = \\|a\\|^2" background="true" derivation="true">
     <p>
       Using the coordinate expression <a
-      href="rvv.html#rvv-es">#rvv-es</a> gives:
+      href="#rvv-es">#rvv-es</a> gives:
 
       <DisplayEquation equation="      \\vec{a} \\cdot \\vec{a}      = a_1 a_1 + a_2 a_2 + a_3 a_3 = \\|a\\|^2." />
     </p>
@@ -195,7 +195,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   <DisplayEquation id="rvi-ei" title="Dot product bi-linearity." equation="\\begin{aligned} \\vec{a} \\cdot(\\vec{b} + \\vec{c}) &amp;=\\vec{a} \\cdot \\vec{b} + \\vec{a}\\cdot \\vec{c} \\\\ (\\vec{a} +\\vec{b}) \\cdot \\vec{c} &amp;=\\vec{a} \\cdot \\vec{c} + \\vec{b}\\cdot \\vec{c} \\\\ \\vec{a} \\cdot (\\beta\\vec{b}) &amp;= \\beta (\\vec{a} \\cdot\\vec{b}) = (\\beta \\vec{a}) \\cdot\\vec{b}\\end{aligned}" background="true" derivation="true">
     <p>
       Using the coordinate expression <a
-      href="rvv.html#rvv-es">#rvv-es</a> gives:
+      href="#rvv-es">#rvv-es</a> gives:
 
       <DisplayEquation equation="\\begin{aligned}      \\vec{a} \\cdot (\\vec{b} + \\vec{c})      &amp;= a_1 (b_1 + c_1) + a_2 (b_2 + c_2) + a_3 (b_3 + c_3) \\\\      &amp;= (a_1 b_1 + a_2 b_2 + a_3 b_3) + (a_1 c_1 + a_2 c_2 + a_3 c_3) \\\\      &amp;= \\vec{a} \\cdot \\vec{b} + \\vec{a} \\cdot \\vec{c} \\\\      (\\vec{a} + \\vec{b}) \\cdot \\vec{c}      &amp;= (a_1 + b_1) c_1 + (a_2 + b_2) c_2 + (a_3 + b_3) c_3 \\\\      &amp;= (a_1 c_1 + a_2 c_2 + a_3 c_3) + (b_1 c_1 + a_2 c_2 + a_3 c_3) \\\\      &amp;= \\vec{a} \\cdot \\vec{c} + \\vec{b} \\cdot \\vec{c} \\\\      \\vec{a} \\cdot (\\beta \\vec{b})      &amp;= a_1 (\\beta b_1) + a_2 (\\beta b_2) + a_3 (\\beta b_3) \\\\      &amp;= \\beta (a_1 b_1 + a_2 b_2 + a_3 b_3) \\\\      &amp;= \\beta (\\vec{a} \\cdot \\vec{b}) \\\\      &amp;= (\\beta a_1) b_1 + (\\beta a_2) b_2 + (\\beta a_3) b_3 \\\\      &amp;= (\\beta \\vec{a}) \\cdot \\vec{b}.      \\end{aligned}" />
     </p>
@@ -273,7 +273,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
 
     <DisplayEquation id="rvv-el2" title="Cross product length." equation="\\| \\vec{a} \\times \\vec{b} \\| = a b \\sin\\theta" background="true" derivation="true">
       <p>
-        Using <a href="rvi.html#rvi-el">Lagrange's identity</a> we can calculate:
+        Using <a href="https://en.wikipedia.org/wiki/Lagrange%27s_identity"  target="_blank">Lagrange's identity</a> we can calculate:
 
         <DisplayEquation equation="\\begin{aligned}        \\| \\vec{a} \\times \\vec{b} \\|^2        &amp;= \\|\\vec{a}\\|^2 \\|\\vec{b}\\|^2        - (\\vec{a} \\cdot \\vec{b})^2 \\\\        &amp;= a^2 b^2 - (a b \\cos\\theta)^2 \\\\        &amp;= a^2 b^2 (1 - \\cos^2\\theta) \\\\        &amp;= a^2 b^2 \\sin^2\\theta.        \\end{aligned}" />
 
@@ -317,7 +317,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   <DisplayEquation id="rvi-ea" title="Cross product anti-symmetry." equation="\\begin{aligned} \\vec{a} \\times\\vec{b} = - \\vec{b} \\times\\vec{a}\\end{aligned}" background="true" derivation="true">
     <p>
       Writing the component expression <a
-      href="rvv.html#rvv-ex">#rvv-ex</a> gives:
+      href="#rvv-ex">#rvv-ex</a> gives:
 
       <DisplayEquation equation="\\begin{aligned}      \\vec{a} \\times \\vec{b}      &amp;= (a_2 b_3 - a_3 b_2) \\,\\hat{\\imath}      + (a_3 b_1 - a_1 b_3) \\,\\hat{\\jmath}      + (a_1 b_2 - a_2 b_1) \\,\\hat{k} \\\\      &amp;= -(a_3 b_2 - a_2 b_3) \\,\\hat{\\imath}      - (a_1 b_3 - a_3 b_1) \\,\\hat{\\jmath}      - (a_2 b_1 - a_1 b_2) \\,\\hat{k} \\\\      &amp;= -\\vec{b} \\times \\vec{a}.      \\end{aligned}" />
     </p>
@@ -335,7 +335,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   <DisplayEquation id="rvi-eb2" title="Cross product bi-linearity." equation="\\begin{aligned}\\vec{a} \\times (\\vec{b} + \\vec{c})&amp;= \\vec{a} \\times \\vec{b} + \\vec{a} \\times \\vec{c} \\\\(\\vec{a} + \\vec{b}) \\times \\vec{c}&amp;= \\vec{a} \\times \\vec{c} + \\vec{b} \\times \\vec{c} \\\\\\vec{a} \\times (\\beta \\vec{b})&amp;= \\beta (\\vec{a} \\times \\vec{b})= (\\beta \\vec{a}) \\times \\vec{b}\\end{aligned}" background="true" derivation="true">
     <p>
       Writing the component expression <a
-      href="rvv.html#rvv-ex">#rvv-ex</a> for the first
+      href="#rvv-ex">#rvv-ex</a> for the first
       equation gives:
 
       <DisplayEquation equation="\\begin{aligned}      \\vec{a} \\times (\\vec{b} + \\vec{c})      &amp;= (a_2 (b_3 + c_3) - a_3 (b_2 + c_2)) \\,\\hat{\\imath} \\\\      &amp;\\quad + (a_3 (b_1 + c_1) - a_1 (b_3 + c_3)) \\,\\hat{\\jmath} \\\\      &amp;\\quad + (a_1 (b_2 + c_2) - a_2 (b_1 + c_1)) \\,\\hat{k} \\\\      &amp;= \\Big((a_2 b_3 - a_3 b_2) \\,\\hat{\\imath}      + (a_3 b_1 - a_1 b_3) \\,\\hat{\\jmath}      + (a_1 b_2 - a_2 b_1) \\,\\hat{k} \\Big) \\\\      &amp;\\quad + \\Big((a_2 c_3 - a_3 c_2) \\,\\hat{\\imath}      + (a_3 c_1 - a_1 c_3) \\,\\hat{\\jmath}      + (a_1 c_2 - a_2 c_1) \\,\\hat{k} \\Big) \\\\      &amp;= \\vec{a} \\times \\vec{b} + \\vec{a} \\times \\vec{c}. \\\\      \\end{aligned}" />
@@ -581,8 +581,8 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         When we differentiate a vector by differentiating each
         component and leaving the basis vectors unchanged, we
         are assuming that the basis vectors themselves are not
-        changing with time. If they are, then we need to <a
-        href="rkv.html#rkv-sb">take this into account</a> as
+        changing with time. If they are, then we need to
+        take this into account as
         well.
       </p>
     </Warning>
diff --git a/src/pages/dyn/vectors.astro b/src/pages/dyn/vectors.astro
index 46176ab2..0a5682a7 100644
--- a/src/pages/dyn/vectors.astro
+++ b/src/pages/dyn/vectors.astro
@@ -158,7 +158,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
                 coordinate system we are using, and which order the
                 coordinates are in. We will typically write the coordinate
                 values explicitly to avoid confusion. This also applies to
-                <a href="rvv.html#rvv-ic">vector components</a>.
+                vector components.
               </p>
         </CalloutCard>
 
@@ -215,8 +215,8 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
 
     <p>
         The two common extensions of polar coordinates to 3D are
-        <a href="rvy.html">cylindrical coordinates</a> and <a
-        href="rvs.html">spherical coordinates</a>.
+        <a href="#cylindrical_coordinates">cylindrical coordinates</a> and <a
+        href="#spherical_coordinates">spherical coordinates</a>.
       </p>
 
     <Center>
@@ -232,7 +232,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         To define polar coordinates, we relate them to another known
         coordinate system, typically Cartesian coordinates as
         follows, where we use the <a
-        href="rvp.html#rvp-it">atan2</a> function.
+        href="http://en.wikipedia.org/wiki/Atan2"  target="_blank">atan2</a> function.
       </p>
 
     <DisplayEquation title="Conversion between polar and Cartesian coordinates" id="rvp-ep" equation = "\\begin{aligned}x &amp;= r \\cos\\theta&amp; r &amp;= \\sqrt{x^2 + y^2} \\\\y &amp;= r \\sin\\theta&amp; \\theta &amp;= \\operatorname{atan2}(y, x)\\end{aligned}" background="True"/>
@@ -450,8 +450,8 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <CalloutContainer slot=cards>
       <CalloutCard title="Notation note">
         <p>
-          Just <a href="rvp.html#rvp-ic">as for position
-          coordinates</a>, we can write the vector components
+          Just as for position
+          coordinates, we can write the vector components
           \(3\hat\imath + 2\hat\jmath\) as the ordered list \((3, 2)\)
           if we know which basis we are using. Because we often will
           be using several bases simultaneously, we will generally
@@ -745,8 +745,8 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
       <p>
         Compute the cross product <InlineEquation equation="\\vec{a} \\times \\vec{b}" />
         using: (1) the angle formula <a
-        href="#rvv-el">#rvv-el</a>; (2) the component formula
-        <a href="#rvv-ex">#rvv-ex</a> with <InlineEquation equation="\\vec{a}, \\vec{b}" />
+        href="/dyn/vector_calculus#rvv-el">#rvv-el</a>; (2) the component formula
+        <a href="/dyn/vector_calculus#rvv-ex">#rvv-ex</a> with <InlineEquation equation="\\vec{a}, \\vec{b}" />
         both in the <InlineEquation equation="\\hat\\imath,\\hat\\jmath" /> basis, both in the
         <InlineEquation equation="\\hat{u}, \\hat{v}" /> basis, and with <InlineEquation equation="\\vec{a}" /> in the
         <InlineEquation equation="\\hat\\imath,\\hat\\jmath" /> basis and <InlineEquation equation="\\vec{b}" /> in the
@@ -758,13 +758,13 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
           (1) The dot product is <InlineEquation equation="\\vec{a} \\cdot \\vec{b} = 7" />
           and the vector lengths are \(a = 3.6\) and \(b = 3.2\),
           so \(\cos\theta = 7 / (ab)\) and \(\theta \approx
-          53^\circ\). Now using <a href="#rvv-el">#rvv-el</a>
+          53^\circ\). Now using <a href="/dyn/vector_calculus#rvv-el">#rvv-el</a>
           gives:
 
           <DisplayEquation equation="\\begin{aligned}          \\vec{a} \\times \\vec{b} &amp;= a b \\sin\\theta ( -\\hat{k}) \\\\          &amp;\\approx -9 \\hat{k}.          \\end{aligned}" />
 
           (2) Using the component formula <a
-          href="#rvv-ex">#rvv-ex</a> gives:
+          href="/dyn/vector_calculus#rvv-ex">#rvv-ex</a> gives:
 
           <DisplayEquation equation="\\begin{aligned}          (3\\hat\\imath + 2\\hat\\jmath) \\times (3\\hat\\imath - \\hat\\jmath)          &amp;= -3 \\hat\\imath \\times \\hat\\jmath + 6 \\hat\\jmath \\times \\hat\\imath \\\\          &amp;= -3 \\hat{k} - 6 \\hat{k} \\\\          &amp;= -9 \\hat{k} \\\\          (3.5 \\hat{u} - 0.7 \\hat{v}) \\times (1.4 \\hat{u} - 2.8 \\hat{v})          &amp;= - (3.5 \\times 2.8) \\hat{u} \\times \\hat{v}          - (0.7 \\times 1.4) \\hat{v} \\times \\hat{u} \\\\          &amp;= -10 \\hat{k} + \\hat{k} \\\\          &amp;= -9 \\hat{k} \\\\          (3\\hat\\imath + 2\\hat\\jmath) \\times (1.4\\hat{u} - 2.8\\hat{v})          &amp;= (3 \\times 1.4) \\hat\\imath \\times \\hat{u}          - (3 \\times 2.8) \\hat\\imath \\times \\hat{v} \\\\          &amp;\\quad + (2 \\times 1.4) \\hat\\jmath \\times \\hat{u}          - (2 \\times 2.8) \\hat\\jmath \\times \\hat{v} \\\\          &amp;= 4.2 \\sin 53^\\circ \\, \\hat{k}          - 8.5 \\sin 143^\\circ \\, \\hat{k} \\\\          &amp;\\quad - 2.8 \\sin 53^\\circ \\, \\hat{k}          - 5.7 \\sin 53^\\circ \\, \\hat{k} \\\\          &amp;= - 9 \\hat{k}.          \\end{aligned}" />
         </p>
@@ -773,7 +773,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
 
     <Example id="rvv-xd" title="Dot product is independent of basis." solution=false>
       <p>
-        Equation <a href="#rvv-ed">#rvv-ed</a> makes
+        Equation <a href="/dyn/vector_calculus#rvv-ed">#rvv-ed</a> makes
         it clear that the dot product does not depend on
         which basis we use to write <InlineEquation equation="\\vec{a}" /> and
         <InlineEquation equation="\\vec{b}" />, so long as we use the same
@@ -785,14 +785,14 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
       </p>
       <p>
         However, we can also verify directly that the component
-        equation <a href="#rvv-es">#rvv-es</a> for the dot
+        equation <a href="/dyn/vector_calculus#rvv-es">#rvv-es</a> for the dot
         product does not depend on which basis we use. To keep
         the algebra short, we will only do this in 2D.
       </p>
       <p>
         We compute the dot product using <a
-        href="#rvv-es">#rvv-es</a> in the
-        $\hat\imath,\hat\jmath$ basis and substitute in the
+        href="/dyn/vector_calculus#rvv-es">#rvv-es</a> in the
+        \(\hat\imath,\hat\jmath\) basis and substitute in the
         change-of-basis expressions <a
         href="#rvv-eg">#rvv-eg</a>, giving:
       </p>
@@ -872,7 +872,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
 
       <p>
         We start with the dot product expression <a
-        href="rvv.html#rvv-ed">#rvv-ed</a> for length and
+        href="/dyn/vector_calculus#rvv-ed">#rvv-ed</a> for length and
         differentiate it:
       </p>
       <DisplayEquation equation="\\begin{aligned} a &amp;= \\sqrt{\\vec{a} \\cdot        \\vec{a}} \\\\ \\frac{d}{dt} a &amp;= \\frac{d}{dt}        \\big( (\\vec{a} \\cdot \\vec{a})^{1/2}        \\big) \\\\ \\dot{a} &amp;= \\frac{1}{2} (\\vec{a}        \\cdot \\vec{a})^{-1/2} (\\dot{\\vec{a}}        \\cdot \\vec{a} + \\vec{a} \\cdot        \\dot{\\vec{a}}) \\\\ &amp;= \\frac{1}{2\\sqrt{a^2}}        (2 \\dot{\\vec{a}} \\cdot \\vec{a}) \\\\        &amp;= \\dot{\\vec{a}} \\cdot        \\hat{a}.\\end{aligned}" />
@@ -881,14 +881,14 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <DisplayEquation title="Derivative of vector direction." background="True" id="rvc-eu" equation="\\dot{\\hat{a}} = \\frac{1}{a}\\operatorname{Comp}(\\dot{\\vec{a}}, \\vec{a})" derivation=True>
       <p>
         We take the definition <a
-        href="rvv.html#rvv-eu">#rvv-eu</a> for the unit vector
+        href="/dyn/vector_calculus#rvv-eu">#rvv-eu</a> for the unit vector
         and differentiate it:
       </p>
       <p>
         <DisplayEquation equation="\\begin{aligned} \\hat{a} &amp;=        \\frac{\\vec{a}}{a} \\\\ \\frac{d}{dt} \\hat{a}        &amp;=        \\frac{d}{dt}\\left(\\frac{\\vec{a}}{a}\\right) \\\\        \\dot{\\hat{a}} &amp;= \\frac{\\dot{\\vec{a}} a -        \\vec{a} \\dot{a}}{a^2} \\\\ &amp;=        \\frac{\\dot{\\vec{a}}}{a} -        \\frac{\\dot{\\vec{a}} \\cdot \\hat{a}}{a^2}        \\vec{a} \\\\ &amp;= \\frac{1}{a} \\big(        \\dot{\\vec{a}} - (\\dot{\\vec{a}} \\cdot        \\hat{a}) \\hat{a} \\big)\\\\ &amp;= \\frac{1}{a}        \\operatorname{Comp}(\\dot{\\vec{a}},        \\vec{a}).\\end{aligned}" />
 
         Here we observed at the end that we had the expression
-        <a href="rvv.html#rvv-em">#rvv-em</a> for the
+        <a href="/dyn/vector_calculus#rvv-em">#rvv-em</a> for the
         complementary projection of the derivative
         <InlineEquation equation="\\dot{\\vec{a}}" /> with respect to <InlineEquation equation="\\vec{a}" />  itself.
       </p>
@@ -905,14 +905,14 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
         From <a href="#rvc-eu">#rvc-eu</a> we know that
         <InlineEquation equation="\\dot{\\hat{a}}" /> is in the direction of <InlineEquation equation="\\operatorname{Comp}(\\dot{\\vec{a}}, \\vec{a})" />
         , and from
-        <a href="rvv.html#rvv-er">#rvv-er</a> we know that this
+        <a href="/dyn/vector_calculus#rvv-er">#rvv-er</a> we know that this
         is orthogonal to <InlineEquation equation="\\vec{a}" /> (and also <InlineEquation equation="\\hat{a}" />).
       </p>
     </DisplayEquation>
 
     <p>
       Recall that we can always write a vector as the <a
-      href="rvv.html#rvv-ei">product of its length and
+      href="/dyn/vector_calculus#rvv-ei">product of its length and
       direction</a>, so <InlineEquation equation="\\vec{a} = a \\hat{a}" />. This gives the
       following decomposition of the derivative of <InlineEquation equation="\\vec{a}" />.
     </p>
@@ -920,7 +920,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <DisplayEquation title="Vector derivative decomposition." background="True" id="rvc-em2" equation="\\begin{aligned} \\dot{\\vec{a}} &amp;=\\underbrace{\\dot{a}\\hat{a}}_{\\operatorname{Proj}(\\dot{\\vec{a}},\\vec{a})} + \\underbrace{a\\dot{\\hat{a}}}_{\\operatorname{Comp}(\\dot{\\vec{a}},\\vec{a})}\\end{aligned}" derivation=True>
       <p>
         Differentiating <InlineEquation equation="\\vec{a} = a \\hat{a}" /> and substituting
-        in <a href="#rvv-el">#rvv-el</a> and <a
+        in <a href="/dyn/vector_calculus#rvv-el">#rvv-el</a> and <a
         href="#rvv-eu">#rvv-eu</a> gives
 
         <DisplayEquation equation="\\begin{aligned}        \\dot{\\vec{a}}        &amp;= \\dot{a} \\hat{a} + a \\dot{\\hat{a}} \\\\        &amp;= ( \\dot{\\vec{a}} \\cdot \\hat{a} ) \\hat{a} + a        \\frac{1}{a} \\operatorname{Comp}(\\dot{\\vec{a}}, \\hat{a}) \\\\        &amp;= \\operatorname{Proj}(\\dot{\\vec{a}}, \\vec{a})        + \\operatorname{Comp}(\\dot{\\vec{a}}, \\vec{a}).        \\end{aligned}" />
@@ -943,7 +943,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
           Vector derivatives can be decomposed into length changes
           (projection onto <InlineEquation equation="\\vec{a}" />) and direction changes
           (complementary projection). Compare to Figure <a
-          href="rvv.html#rvv-fu">#rvv-fu</a>.
+          href="/dyn/vector_calculus#rvv-fu">#rvv-fu</a>.
         </p>
       </PrairieDrawCanvas>
     </Center>
@@ -1059,7 +1059,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     Spherical coordinates are defined with respect to a set of
     Cartesian coordinates, and can be converted to and from
     these coordinates using the <a
-    href="rvp.html#rvp-it">atan2</a> function as follows.
+    href="http://en.wikipedia.org/wiki/Atan2"  target="_blank">atan2</a> function as follows.
   </p>
 
   <DisplayEquation title="Conversion between spherical and Cartesian coordinates." background="True" id="rvs-ec" equation="\\begin{aligned}x &amp;= r \\cos\\theta \\sin\\phi &amp; r &amp;= \\sqrt{x^2 + y^2 + z^2} \\\\y &amp;= r \\sin\\theta \\sin\\phi &amp; \\theta &amp;= \\operatorname{atan2}(y, x) \\\\z &amp;= r \\cos\\phi &amp; \\phi &amp;= \\operatorname{arccos}(z / r)\\end{aligned}" derivation=True>
@@ -1074,7 +1074,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
           To convert from Cartesian coordinates, we use the same
           projection and read off the expressions for the
           spherical coordinates. This uses the <a
-          href="rvp.html#rvp-it">atan2</a> function to handle the
+          href="http://en.wikipedia.org/wiki/Atan2"  target="_blank">atan2</a> function to handle the
           different quadrants for \(\theta\).
         </p>
       </Col>
@@ -1449,7 +1449,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
 
     <p>
       Geographic coordinates are typically given
-      in <a href="rvs.html">spherical coordinates</a>, but without
+      in <a href="#spherical_coordinates">spherical coordinates</a>, but without
       the radius and with the angles given
       in <a target="_blank" rel="noopener noreferrer" href="http://en.wikipedia.org/wiki/Arcminute">degrees,
       minutes, and seconds</a>, with the latitude first, and the
@@ -1481,8 +1481,8 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     <CalloutContainer slot="cards">
       <CalloutCard title="Reference material">
         <ul>
-          <li><a href="rvv.html#rvv-sd">Dot product</a></li>
-          <li><a href="rvs.html">Spherical coordinates</a></li>
+          <li><a href="/dyn/vector_calculus#dot_product">Dot product</a></li>
+          <li><a href="#spherical_coordinates">Spherical coordinates</a></li>
         </ul>
       </CalloutCard>
       <CalloutCard>
@@ -1517,8 +1517,8 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
     the origin. The shortest distance calculation thus reduces
     to finding the angle between the vectors <InlineEquation equation="\\vec{OA}" /> and
     <InlineEquation equation="\\vec{OB}" />, which can be easily done by finding their <a
-    href="rvv.html#rvv-sd">dot product</a> after changing them
-    to <a href="rvs.html#rvs-ec">rectangular coordinates</a>.
+    href="/sta/vector_calculus#rvv-sd">dot product</a> after changing them
+    to <a href="#cartesian_coordinates">rectangular coordinates</a>.
   </p>
   <Center>
   <PrairieDrawCanvas id="aos-fd-c" width="600" height="600">
@@ -1633,7 +1633,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   <p>
     Given any two points <InlineEquation equation="A" /> and <InlineEquation equation="B" /> on the surface of the
     Earth, we choose coordinate axes and use <a
-    href="rvs.html">spherical coordinates</a> so that <InlineEquation equation="A" /> is at
+    href="#spherical_coordinates">spherical coordinates</a> so that <InlineEquation equation="A" /> is at
     <InlineEquation equation="(r = r_0, \\theta = 0, \\phi = \\pi - \\phi_0)" /> and <InlineEquation equation="B" /> is at
     <InlineEquation equation="(r = r_0, \\theta = 0, \\phi = \\pi + \\phi_0)" />. Here <InlineEquation equation="r_0" /> is
     the radius of the Earth and <InlineEquation equation="0 \\le \\phi_0 \\le \\pi/2" />. The
@@ -1658,14 +1658,14 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
   </p>
   <p>
     To switch from rectangular to spherical coordinates we use
-    the <a href="rvs.html#rvs-ec">conversion</a>:
+    the <a href="#rvs-ec">conversion</a>:
   </p>
   <p>
     <DisplayEquation equation="\\begin{aligned}    x &amp;= r \\cos\\theta \\sin\\phi \\\\    y &amp;= r \\sin\\theta \\sin\\phi \\\\    z &amp;= r \\cos\\phi.    \\end{aligned}" />
   </p>
   <p>
     Differentiating these expressions and substituting (or using
-    the <a href="rvs.html#rvs-ep">spherical velocity
+    the <a href="#rvs-ep">spherical velocity
     expression</a>) gives the path length expression:
   </p>
   <p>
diff --git a/src/pages/sta/vectors_scalars.astro b/src/pages/sta/vectors_scalars.astro
index 72f5cda1..094198fd 100644
--- a/src/pages/sta/vectors_scalars.astro
+++ b/src/pages/sta/vectors_scalars.astro
@@ -287,7 +287,7 @@ Alternatively, the vector components can be determined geometrically via the ang
     product</em> or <em>scalar product</em>) is defined by
   </p>
 
-<DisplayEquation equation="\\vec{a} \\cdot \\vec{b}= a_1 b_1 + a_2 b_2 + a_3 b_3" title="Dot product from components." background="True"/>
+<DisplayEquation equation="\\vec{a} \\cdot \\vec{b}= a_1 b_1 + a_2 b_2 + a_3 b_3" title="Dot product from components." background="True" id="rvv-es"/>
 
 <p>
     An alternative expression for the dot product can be
@@ -403,7 +403,7 @@ Alternatively, the vector components can be determined geometrically via the ang
 <DisplayEquation id="rvi-ed" title="Dot product symmetry." equation="\\vec{a} \\cdot \\vec{b} = \\vec{b} \\cdot \\vec{a}" background="true" derivation="true">
 <p>
   Using the coordinate expression <a
-  href="rvv.html#rvv-es">#rvv-es</a> gives:
+  href="#rvv-es">#rvv-es</a> gives:
 
   <DisplayEquation equation="      \\vec{a} \\cdot \\vec{b}      = a_1 b_1 + a_2 b_2 + a_3 b_3      = b_1 a_1 + b_2 a_2 + b_3 a_3      = \\vec{b} \\cdot \\vec{a}." />
 </p>
@@ -412,7 +412,7 @@ Alternatively, the vector components can be determined geometrically via the ang
 <DisplayEquation id="rvi-eg" title="Dot product vector length." equation="\\vec{a} \\cdot \\vec{a} = \\|a\\|^2" background="true" derivation="true">
 <p>
   Using the coordinate expression <a
-  href="rvv.html#rvv-es">#rvv-es</a> gives:
+  href="#rvv-es">#rvv-es</a> gives:
 
   <DisplayEquation equation="      \\vec{a} \\cdot \\vec{a}      = a_1 a_1 + a_2 a_2 + a_3 a_3 = \\|a\\|^2." />
 </p>
@@ -421,7 +421,7 @@ Alternatively, the vector components can be determined geometrically via the ang
 <DisplayEquation id="rvi-ei" title="Dot product bi-linearity." equation="\\begin{aligned} \\vec{a} \\cdot(\\vec{b} + \\vec{c}) &amp;=\\vec{a} \\cdot \\vec{b} + \\vec{a}\\cdot \\vec{c} \\\\ (\\vec{a} +\\vec{b}) \\cdot \\vec{c} &amp;=\\vec{a} \\cdot \\vec{c} + \\vec{b}\\cdot \\vec{c} \\\\ \\vec{a} \\cdot (\\beta\\vec{b}) &amp;= \\beta (\\vec{a} \\cdot\\vec{b}) = (\\beta \\vec{a}) \\cdot\\vec{b}\\end{aligned}" background="true" derivation="true">
 <p>
   Using the coordinate expression <a
-  href="rvv.html#rvv-es">#rvv-es</a> gives:
+  href="#rvv-es">#rvv-es</a> gives:
 
   <DisplayEquation equation="\\begin{aligned}      \\vec{a} \\cdot (\\vec{b} + \\vec{c})      &amp;= a_1 (b_1 + c_1) + a_2 (b_2 + c_2) + a_3 (b_3 + c_3) \\\\      &amp;= (a_1 b_1 + a_2 b_2 + a_3 b_3) + (a_1 c_1 + a_2 c_2 + a_3 c_3) \\\\      &amp;= \\vec{a} \\cdot \\vec{b} + \\vec{a} \\cdot \\vec{c} \\\\      (\\vec{a} + \\vec{b}) \\cdot \\vec{c}      &amp;= (a_1 + b_1) c_1 + (a_2 + b_2) c_2 + (a_3 + b_3) c_3 \\\\      &amp;= (a_1 c_1 + a_2 c_2 + a_3 c_3) + (b_1 c_1 + a_2 c_2 + a_3 c_3) \\\\      &amp;= \\vec{a} \\cdot \\vec{c} + \\vec{b} \\cdot \\vec{c} \\\\      \\vec{a} \\cdot (\\beta \\vec{b})      &amp;= a_1 (\\beta b_1) + a_2 (\\beta b_2) + a_3 (\\beta b_3) \\\\      &amp;= \\beta (a_1 b_1 + a_2 b_2 + a_3 b_3) \\\\      &amp;= \\beta (\\vec{a} \\cdot \\vec{b}) \\\\      &amp;= (\\beta a_1) b_1 + (\\beta a_2) b_2 + (\\beta a_3) b_3 \\\\      &amp;= (\\beta \\vec{a}) \\cdot \\vec{b}.      \\end{aligned}" />
 </p>
@@ -500,7 +500,7 @@ Alternatively, the vector components can be determined geometrically via the ang
 
   <DisplayEquation id="rvv-el2" title="Cross product length." equation="\\| \\vec{a} \\times \\vec{b} \\| = a b \\sin\\theta" background="true" derivation="true">
     <p>
-      Using <a href="rvi.html#rvi-el">Lagrange's identity</a> we can calculate:
+      Using <a href="https://en.wikipedia.org/wiki/Lagrange%27s_identity" target="_blank">Lagrange's identity</a> we can calculate:
 
       <DisplayEquation equation="\\begin{aligned}        \\| \\vec{a} \\times \\vec{b} \\|^2        &amp;= \\|\\vec{a}\\|^2 \\|\\vec{b}\\|^2        - (\\vec{a} \\cdot \\vec{b})^2 \\\\        &amp;= a^2 b^2 - (a b \\cos\\theta)^2 \\\\        &amp;= a^2 b^2 (1 - \\cos^2\\theta) \\\\        &amp;= a^2 b^2 \\sin^2\\theta.        \\end{aligned}" />
 
@@ -544,7 +544,7 @@ Alternatively, the vector components can be determined geometrically via the ang
 <DisplayEquation id="rvi-ea" title="Cross product anti-symmetry." equation="\\begin{aligned} \\vec{a} \\times\\vec{b} = - \\vec{b} \\times\\vec{a}\\end{aligned}" background="true" derivation="true">
   <p>
     Writing the component expression <a
-    href="rvv.html#rvv-ex">#rvv-ex</a> gives:
+    href="#rvv-ex">#rvv-ex</a> gives:
 
     <DisplayEquation equation="\\begin{aligned}      \\vec{a} \\times \\vec{b}      &amp;= (a_2 b_3 - a_3 b_2) \\,\\hat{\\imath}      + (a_3 b_1 - a_1 b_3) \\,\\hat{\\jmath}      + (a_1 b_2 - a_2 b_1) \\,\\hat{k} \\\\      &amp;= -(a_3 b_2 - a_2 b_3) \\,\\hat{\\imath}      - (a_1 b_3 - a_3 b_1) \\,\\hat{\\jmath}      - (a_2 b_1 - a_1 b_2) \\,\\hat{k} \\\\      &amp;= -\\vec{b} \\times \\vec{a}.      \\end{aligned}" />
   </p>
@@ -562,7 +562,7 @@ Alternatively, the vector components can be determined geometrically via the ang
 <DisplayEquation id="rvi-eb2" title="Cross product bi-linearity." equation="\\begin{aligned}\\vec{a} \\times (\\vec{b} + \\vec{c})&amp;= \\vec{a} \\times \\vec{b} + \\vec{a} \\times \\vec{c} \\\\(\\vec{a} + \\vec{b}) \\times \\vec{c}&amp;= \\vec{a} \\times \\vec{c} + \\vec{b} \\times \\vec{c} \\\\\\vec{a} \\times (\\beta \\vec{b})&amp;= \\beta (\\vec{a} \\times \\vec{b})= (\\beta \\vec{a}) \\times \\vec{b}\\end{aligned}" background="true" derivation="true">
   <p>
     Writing the component expression <a
-    href="rvv.html#rvv-ex">#rvv-ex</a> for the first
+    href="#rvv-ex">#rvv-ex</a> for the first
     equation gives:
 
     <DisplayEquation equation="\\begin{aligned}      \\vec{a} \\times (\\vec{b} + \\vec{c})      &amp;= (a_2 (b_3 + c_3) - a_3 (b_2 + c_2)) \\,\\hat{\\imath} \\\\      &amp;\\quad + (a_3 (b_1 + c_1) - a_1 (b_3 + c_3)) \\,\\hat{\\jmath} \\\\      &amp;\\quad + (a_1 (b_2 + c_2) - a_2 (b_1 + c_1)) \\,\\hat{k} \\\\      &amp;= \\Big((a_2 b_3 - a_3 b_2) \\,\\hat{\\imath}      + (a_3 b_1 - a_1 b_3) \\,\\hat{\\jmath}      + (a_1 b_2 - a_2 b_1) \\,\\hat{k} \\Big) \\\\      &amp;\\quad + \\Big((a_2 c_3 - a_3 c_2) \\,\\hat{\\imath}      + (a_3 c_1 - a_1 c_3) \\,\\hat{\\jmath}      + (a_1 c_2 - a_2 c_1) \\,\\hat{k} \\Big) \\\\      &amp;= \\vec{a} \\times \\vec{b} + \\vec{a} \\times \\vec{c}. \\\\      \\end{aligned}" />