A-LevelMathematicsVectors9709/32 · May/June 2021 · Q1110 Marks

With respect to the origin O, the points A and B have position vectors given by OA = 2i – j and OB = j – 2k.

(a)Show that OA = OB and use a scalar product to calculate angle AOB in degrees.[4]
(b)Find the possible position vectors of P.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[B1] Show that OA = OB = √5
[M1] Evaluate the scalar product of the correct position vectors
[M1] Divide their scalar product by the product of the moduli of their vectors and evaluate the inverse cosine of the result
[A1] Obtain answer 101.5°
[B1] State or imply M has position vector i – k
[M1] Taking a general point of OM to have position vector λi – λk, express AP = √7 OA as an equation in λ
[A1] State a correct equation in any form
[A1] Reduce to λ² – 2λ − 15 = 0
[DM1] Solve a quadratic and state a position vector
[A1] Obtain answers 5i – 5k and −3i + 3k

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Topic: Vectors, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source: A-Level Mathematics, May/June 2021 Paper 3 Variant 2, question 11.

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