A-LevelMathematicsVectors9709/12 · May/June 2013 · Q67 Marks
Relative to an origin O, the position vectors of points A and B are given by OA = i - 2j + 2k and OB = 3i + pj + qk, where p and q are constants.
- (i)State the values of p and q for which OA is parallel to OB.[2]
- (ii)In the case where q = 2p, find the value of p for which angle BOA is 90°.[2]
- (iii)In the case where p = 1 and q = 8, find the unit vector in the direction of AB.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [1] B1 For (i): p = -6
- [1] B1 For (i): q = 6
- [1] M1 For (ii): Uses the dot product of OA and OB equals 0 (3 - 2p + 4p = 0)
- [1] A1 For (ii): Correct value of p = -1.5
- [1] B1 For (iii): Correct vector AB = (2i + 3j + 6k)
- [1] M1 For (iii): Divides vector AB by its modulus (magnitude)
- [1] A1 For (iii): Correct unit vector (2i + 3j + 6k) ÷ 7
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