O-LevelAdditional MathematicsVectors in two dimensions4037/22 · May/June 2018 · Q76 Marks
Vectors i and j are vectors parallel to the x-axis and y-axis respectively. Given that a = 2i + 3j, b = i – 5j and c = 3i + 11j, find
- (i)the exact value of |a + c|,[2]
- (ii)the value of the constant m such that a + mb is parallel to j,[2]
- (iii)the value of the constant n such that na – b = c.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] |their(a + c)| = √their(5² + 14²)
- [A1] √221 mark final answer
- [M1] for attempting to form a + mb and equate the scalar of the i component to 0, e.g. (2 + m)i + (3 – 5m)j, so (2 + m) = 0
- [A1] m = -2 only
- [M1] for attempting to form na - b = c and equate components, e.g. (2n - 1)i + (3n + 5)j = 3i + 11j or n(2i + 3j) = (3i + 11j) + (i – 5j) oe leading to 2n - 1 = 3 or 3n + 5 = 11 oe, soi
- [A1] n = 2 only
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