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A-LevelFurther MathematicsVectors9231/12 · May/June 2024 · Q512 Marks

The points A, B, C have position vectors 2i+2j+4k, 2i+4j-k, -3i-3j+4k, respectively, relative to the origin O. The point D has position vector 2i+j+3k.

  1. (a)Find the equation of the plane ABC, giving your answer in the form ax+by+cz = d.[5]
  2. (b)Find the perpendicular distance from D to the plane ABC.[2]
  3. (c)Find the shortest distance between the lines AB and CD.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [B1] Finds direction vectors of two lines in the plane.
  2. [M1 A1] Finds normal to the plane ABC.
  3. [M1 A1] Substitutes point. AEF for final answer.
  4. [M1 A1] Correct formula for distance from point to plane.
  5. [B1]
  6. [M1 A1] Find common perpendicular.
  7. [M1 A1] Uses formula for shortest distance.

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About this question

Topic
Vectors, A-Level Further Mathematics (syllabus 9231). Structured question, 12 marks.
Source
A-Level Further Mathematics, May/June 2024 Paper 1 Variant 2, question 5.

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