Relative to the origin O, a = 2 i - j + 2 k and b = i + 2 j - 2 k are the position vectors of A and B.
(a) Find a unit vector in the direction of a.
(b) Find angle AOB.
(c) OABC is a parallelogram. Find the position vector of C.
(d) Find |AC⃗|.
From Paper 3: Pure Mathematics and Mechanics
49 marks
In triangle OAB, OA⃗ = a and OB⃗ = b. The point X lies on OA with OX : XA = 2 : 1, and Y is the midpoint of AB.
(a) Find XY⃗ in terms of a and b.
(b) The line XY meets the line OB extended at Z, where OZ⃗ = λ b. Find λ.
Score 0 / 18 · 0 of 2 marked
This paper is written by Plasmo in the style of the OCR A-Level Maths exam. It is not a past paper and is not produced or endorsed by the exam board.