A-LevelFurther MathematicsVectors9231/12 · May/June 2019 · Q38 Marks

The lines l₁ and l₂ have equations r = 6i + 2j + 7k + λ(i + j) and r = 4i + 4j + μ(−6j + k) respectively. The point P on l₁ and the point Q on l₂ are such that PQ is perpendicular to both l₁ and l₂. Find the position vectors of P and Q.

The lines l₁ and l₂ have equations r = 6i + 2j + 7k + λ(i + j) and r = 4i + 4j + μ(−6j + k) respectively. The point P on l₁ and the point Q on l₂ are such that PQ is perpendicular to both l₁ and l₂. Find the position vectors of P and Q.[8]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[2] Finds PQ.
[1] Uses that dot product of PQ with line directions is 0. Or, alternatively, PQ is multiple of common perpendicular.
[1] Deduces one equation. CWO.
[1] Deduces second equation. CWO.
[2] Solves simultaneous equations.
[1] States OP and OQ.

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Topic: Vectors, A-Level Further Mathematics (syllabus 9231). Structured question, 8 marks.
Source: A-Level Further Mathematics, May/June 2019 Paper 1 Variant 2, question 3.

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