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.

Start practising Read the lesson

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
Relative to a fixed origin $O$ , the points $A$ and $B$ have position vectors $3\mathbf{j} - 3\mathbf{k}$ and $6\mathbf{i} + 3\mathbf{k}$ respectively.

The point $P$ lies on the line segment $AB$ and is such that $OP$ is perpendicular to $AB$ .
(a) Find the position vector of $P$ . (5 marks)
(b) Hence find the exact area of triangle $OAB$ . (2 marks)
Level 5 · 7 marksTry it