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A-LevelFurther MathematicsVectors9231/12 · Oct/Nov 2018 · Q1012 Marks

The position vectors of the points A, B, C, D are i + j + 3k, 3i + 4j + 5k, -i + 3k, mj + 4k, respectively, where m is a constant.

  1. (i)Show that the lines AB and CD are parallel when m = 3/2.[1]
  2. (ii)Given that m ≠ 3/2, find the shortest distance between the lines AB and CD.[5]
  3. (iii)When m = 2, find the acute angle between the planes ABC and ABD, giving your answer in degrees.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [B1] Or shows if parallel, then m=3/2
  2. [M1A1] Finds common perpendicular using cross product.
  3. [M1] Uses formula for shortest distance.
  4. [A1]
  5. [M1A1] Finds normal to plane ABC (AEF).
  6. [A1] Finds normal to ABD (AEF).
  7. [M1A1FT] Uses formula for angle between two lines.
  8. [A1] CAO.

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About this question

Topic
Vectors, A-Level Further Mathematics (syllabus 9231). Structured question, 12 marks.
Source
A-Level Further Mathematics, Oct/Nov 2018 Paper 1 Variant 2, question 10.

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