A-LevelMathematicsVectors9709/12 · Oct/Nov 2009 · Q67 Marks
In the diagram, OABCDEFG is a cube in which each side has length 6. Unit vectors i, j and k are parallel to OA, OC and OD respectively. The point P is such that AP = ⅓ AB and the point Q is the mid-point of DF. [Figure X.X]
- (i)Express each of the vectors OQ and PQ in terms of i, j and k.[3]
- (ii)Find the angle OQP.[4]
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 2009). The mark or mark type is shown in brackets.
- [1] OQ = 3i + 3j + 6k (co)
- [2] PQ = -3i + j + 6k (Loses one for each error)
- [1] Use of x₁x₂ + y₁y₂ + z₁z₂ co. (e.g. 30)
- [1] Correct method for modulus (once) and all correctly linked. co.
- [2] θ = 53.0° (M1 for cosine rule, M1 for attempt at 3 sides, A1 for answer)
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →