O-LevelAdditional MathematicsVectors in two dimensions4037/21 · May/June 2012 · Q88 Marks
Relative to an origin O, the position vectors of the points A and B are 2i – 3j and 11i + 9j respectively.
- (i)Write down an expression for AB.[2]
- (ii)The point C lies on AB such that AC = (1/3) AB. Find the length of OC.[4]
- (iii)The point D lies on OA such that DC is parallel to OB. Find the position vector of D.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [2] (i) AB = OB – OA; 9i + 45j A1
- [4] (ii) OC = OA + (1/3)AB M1; OC = 5i + 12j A1; |OC| = √(5² + 12²) M1; 13 A1
- [2] (iii) OD = (2λ)i + (-3λ)j and solve (12+3λ)/(5-2λ) = 42/11 M1; 4/3 i - 2j A1
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