O-LevelAdditional MathematicsVectors in two dimensions4037/12 · Oct/Nov 2022 · Q58 Marks
Find the vector with magnitude 200 in the direction of (7 -24).
- (a)Find the vector with magnitude 200 in the direction of (7 -24).[2]
- (b)The diagram shows triangle AOB such that OA = a, and OB = b. The point C lies on the line AB such that AC : AB = 1:3. Find the vector OC in terms of a and b, giving your answer in its simplest form.[3]
- (c)Given the vector equation p(2 1) + q(2 4) = 5(-p+1 p+q), find the values of p and q.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [1] (a) (7/25 -24/25) seen or implied
- [1] (a) (56 -192) or 8 (7 -24)
- [1] (b) AC = 1/3(b-a) or CB = 2/3(b-a) or equivalent
- [1] (b) For using OA + their AC or OB + their BC or equivalent
- [1] (b) 2/3 a + 1/3 b
- [1] (c) For equating like vectors to obtain at least one equation (e.g. 2p+2q=-5p+5 or p+4q=5p+5q)
- [1] (c) For an attempt to solve their equations to obtain both p and q
- [1] (c) p=-5, q=20 (for both)
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