Vectors worksheet

5 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

5 questions 17 marks Sheet 1

3 marks
The points \(A\) and \(B\) are marked on a coordinate grid.

(a)
Write \(\overrightarrow{AB}\) as a column vector.

(b)
Write \(\overrightarrow{BA}\) as a column vector.
2 marks
The diagram shows \(\overrightarrow{OA} = \mathbf{a}\) and \(\overrightarrow{OB} = \mathbf{b}\) on a grid of unit squares.

Work out \(\mathbf{a} - \mathbf{b}\). Give your answer as a column vector.
4 marks
\(OPQ\) is a triangle.

\(\overrightarrow{OP} = 3\mathbf{a}\) and \(\overrightarrow{OQ} = 3\mathbf{b}\).

(a)
Express \(\overrightarrow{PQ}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).

(b)
Express \(\overrightarrow{QP}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).
4 marks
\(OABC\) is a parallelogram.

\(\overrightarrow{OA} = 2\mathbf{a}\) and \(\overrightarrow{OC} = 3\mathbf{b}\).

(a)
Express \(\overrightarrow{OB}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).

(b)
Express \(\overrightarrow{AC}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).
4 marks
\(OAB\) is a triangle. \(M\) is the midpoint of \(AB\).

\(\overrightarrow{OA} = 2\mathbf{a}\) and \(\overrightarrow{OB} = 2\mathbf{b}\).

(a)
Find \(\overrightarrow{AB}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).

(b)
Find \(\overrightarrow{OM}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\).

Answers

(a) \(\begin{pmatrix} 7 \\ 4 \end{pmatrix}\)
(b) \(\begin{pmatrix} -7 \\ -4 \end{pmatrix}\)
\(\begin{pmatrix} 3 \\ -3 \end{pmatrix}\)
(a) \(3\mathbf{b} - 3\mathbf{a}\)
(b) \(3\mathbf{a} - 3\mathbf{b}\)
(a) \(2\mathbf{a} + 3\mathbf{b}\)
(b) \(3\mathbf{b} - 2\mathbf{a}\)
(a) \(2\mathbf{b} - 2\mathbf{a}\)
(b) \(\mathbf{a} + \mathbf{b}\)