GCSE · Vectors

Column vectorsExam-style questions

A vector is a translation — so far across, so far up — not a place. How to add, subtract and scale columns, why a scalar multiple is parallel, how Pythagoras gives the magnitude, and why the journey from A to B is destination minus start.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    a=(31)\mathbf{a} = \begin{pmatrix} 3 \\ 1 \end{pmatrix} and b=(25)\mathbf{b} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}. Work out a+b\mathbf{a} + \mathbf{b}.
    Level 1 · 1 markTry it
  2. 2
    a=(4−2)\mathbf{a} = \begin{pmatrix} 4 \\ -2 \end{pmatrix}. Work out 3a3\mathbf{a}.
    Level 1 · 1 markTry it
  3. 3
    p=(62)\mathbf{p} = \begin{pmatrix} 6 \\ 2 \end{pmatrix} and q=(14)\mathbf{q} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}. Work out p−q\mathbf{p} - \mathbf{q}.
    Level 1 · 1 markTry it