     [
       "makeVector"
       "C5"
-      "Consider the four vectors$$\\mathbf{A}=\\begin{pmatrix}\\\\-4\\\\-3\\\\0\\end{pmatrix}\\,,\\; \\mathbf{B}=\\begin{pmatrix}\\\\2\\\\-6\\\\0\\end{pmatrix}$$$$\\mathbf{C}=\\begin{pmatrix}\\\\-4\\\\2\\\\5\\end{pmatrix}\\,,\\; \\mathbf{D}=\\begin{pmatrix}\\\\-1\\\\-3\\\\-7\\end{pmatrix}$$<ol class=\"exercise\"><li>Order the vectors by magnitude.</li><li>Use the scalar product to find the angles between<ol class=\"subexercise\"><li>\\(\\mathbf{D}\\) and \\(\\mathbf{A}\\),</li><li>\\(\\mathbf{A}\\) and \\(\\mathbf{C}\\)</li></ol></ol>"
-      "<ol class=\"exercise\"><li>\\(|\\mathbf{D}|=\\sqrt{59},\\) \\(|\\mathbf{C}|=\\sqrt{45},\\) \\( |\\mathbf{B}|=\\sqrt{40}\\) and \\(|\\mathbf{A}|=\\sqrt{25}\\).</li><li><ol class=\"subexercise\"><li>\\(\\arccos\\left(\\frac{13}{25\\sqrt{59}}\\right)\\)</li><li>\\(\\arccos\\left(\\frac{2}{45\\sqrt{5}}\\right)\\)</li></ol></li></ol>"
+      "Consider the four vectors$$\\mathbf{A}=\\begin{pmatrix}-4\\\\-3\\\\0\\end{pmatrix}\\,,\\; \\mathbf{B}=\\begin{pmatrix}2\\\\-6\\\\0\\end{pmatrix}$$$$\\mathbf{C}=\\begin{pmatrix}-4\\\\2\\\\5\\end{pmatrix}\\,,\\; \\mathbf{D}=\\begin{pmatrix}-1\\\\-3\\\\-7\\end{pmatrix}$$<ol class=\"exercise\"><li>Order the vectors by magnitude.</li><li>Use the scalar product to find the angles between<ol class=\"subexercise\"><li>\\(\\mathbf{D}\\) and \\(\\mathbf{A}\\),</li><li>\\(\\mathbf{A}\\) and \\(\\mathbf{C}\\)</li></ol></ol>"
+      "<ol class=\"exercise\"><li>\\(|\\mathbf{D}|=\\sqrt{59},\\) \\(|\\mathbf{C}|=\\sqrt{45},\\) \\( |\\mathbf{B}|=\\sqrt{40}\\) and \\(|\\mathbf{A}|=\\sqrt{25}\\).</li><li><ol class=\"subexercise\"><li>\\(\\arccos\\left(\\frac{13}{5\\sqrt{59}}\\right)\\)</li><li>\\(\\arccos\\left(\\frac{2}{3\\sqrt{5}}\\right)\\)</li></ol></li></ol>"
     ]
     [
       "makeLines"
       "C6"
       "Consider the lines$$3x - 2=y - 2=3z - 3$$and$$2x - 0.6666666666666666=y - 1.3333333333333333=- 2z + 2.6666666666666665$$Find the angle between them<br>and determine whether they<br>intersect."
-      "The angle between the lines is$$\\arccos\\left(\\frac{-36}{36\\sqrt{66}}\\right).$$The lines do not meet."
+      "The angle between the lines is$$\\arccos\\left(\\frac{-6}{\\sqrt{66}}\\right).$$The lines do not meet."
     ]
     [
       "makeIneq2"

    [
      "makeCircle"
      "C16"
      "Find, for a sector of angle \\(\\frac{14\\pi}{8}\\) of a disc of radius \\(6:\\)<br>i. the length of the perimeter; and<br>ii. the area."
      "i. \\(12+\\frac{21}{2}\\pi\\)<br>ii. \\(\\frac{63}{2}\\pi\\)"
    ]
    [

      "makeMatrix3"
      "F7"
      "Let $$A=\\begin{pmatrix}2&3&-2\\\\-1&-1&2\\\\1&0&2\\end{pmatrix} \\qquad \\text{and} \\qquad B=\\begin{pmatrix}1&4&-1\\\\1&-2&1\\\\0&-4&0\\end{pmatrix}$$.Compute: <ul class=\"exercise\"><li>\\(A+B\\)</li><li>\\(A \\times B\\)</li><li>\\(B^{-1}\\)</li></ul>"
      "<ul class=\"exercise\"><li>\\(\\begin{pmatrix}3&7&-3\\\\0&-3&3\\\\1&-4&2\\end{pmatrix}\\)</li><li>\\(\\begin{pmatrix}5&10&1\\\\-2&-10&0\\\\1&-4&-1\\end{pmatrix}\\)</li><li>\\(\\displaystyle \\frac{1}{4}\\textstyle \\begin{pmatrix} 2&2&1\\\\0&0&-1\\\\-2&2&-3\\end{pmatrix}\\)</li></ul>"
    ]
    [
      "makeFurtherVector"
      "F8"
      "Let \\(\\mathbf{a}=\\begin{pmatrix}-2\\\\0\\\\3\\end{pmatrix}\\,\\), \\(\\;\\mathbf{b}=\\begin{pmatrix}-4\\\\3\\\\0\\end{pmatrix}\\,\\) and \\(\\mathbf{c}=\\begin{pmatrix}-3\\\\4\\\\5\\end{pmatrix}\\). Calculate: <ul class=\"exercise\"><li>the vector product, \\(\\mathbf{a}\\wedge \\mathbf{b}\\),</li><li>the scalar triple product, \\([\\mathbf{a}, \\mathbf{b}, \\mathbf{c}]\\).</li></ul>"
      "<ul class=\"exercise\"><li>\\(\\begin{pmatrix}-9\\\\-12\\\\-6\\end{pmatrix}\\)</li><li>\\(-51\\)</li></ul>"
    ]
    [
      "makeNewtonRaphson"
