A-level · Vectors

Position vectorsExam-style questions

Pinning points to the origin with position vectors, the "destination minus start" rule AB = b − a, the distance between two points as |b − a|, the midpoint as ½(a + b), and finding a point that divides a segment in a ratio.

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15 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Points $A$ and $B$ have position vectors $2\mathbf{i} - \mathbf{j} + 3\mathbf{k}$ and $5\mathbf{i} + 3\mathbf{j} - \mathbf{k}$ . Find the exact distance $AB$ .
Level 3 · 3 marksTry it
2
The points $A$ and $B$ have position vectors $\mathbf{a} = 2\mathbf{i} + \mathbf{j}$ and $\mathbf{b} = 8\mathbf{i} + 5\mathbf{j}$ .
(a) Find $\overrightarrow{AB}$ and its magnitude, giving $|\overrightarrow{AB}|$ to 3 s.f. (3 marks)
(b) The point $P$ divides $AB$ in the ratio $1 : 2$ . Find the position vector of $P$ . (4 marks)
Level 3 · 7 marksTry it
3
Relative to a fixed origin $O$ $O$
- the point $A$ has position vector $\mathbf{i} + 3\mathbf{j} - 2\mathbf{k}$
- the point $B$ has position vector $2\mathbf{i} + c\mathbf{j} + 4\mathbf{k}$
where $c$ $c$ is a constant.
(a) Show that $\left|\overrightarrow{OA}\right| = \sqrt{14}$ $O A = 14$

(1 mark)

Given that $\left|\overrightarrow{OB}\right| = 2\left|\overrightarrow{OA}\right|$ $O B = 2 O A$
(b) find the possible values of $c$ $c$ .

(3 marks)
Level 3 · 4 marksTry it