A-LevelMathematicsVectors9709/12 · May/June 2014 · Q77 Marks
The diagram shows a trapezium ABCD in which BA is parallel to CD. The position vectors of A, B and C relative to an origin O are given by O A = (3/4), O B = (3/2) and O C = (4/6). [Figure 7.1]
- (i)Use a scalar product to show that AB is perpendicular to BC.[3]
- (ii)Given that the length of CD is 12 units, find the position vector of D.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [M1] AB = b – a once (a – b is ok)
- [M1] Use of x₁x₂... with AB and CB
- [A1] → –6 – 2 + 8 = 0 → 90° All correct
- [M1] Unit vector = 1/3 (2/1/-2) Method for unit vector.
- [M1] CD = 12 × unit vector = ± (8/4/-8) Knows to multiply by 12 or ±4BA
- [M1 A1] OD = OC + CD = (12/9/-2) Correct method. co
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