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A-LevelFurther MathematicsVectors9231/12 · May/June 2022 · Q210 Marks

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

  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 O to the plane ABC.[2]
  3. (c)The point D has position vector 2i+3j-3k. Find the coordinates of the point of intersection of the line OD with the plane ABC.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2022). 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.
  4. [M1 A1] Divides their constant by magnitude of their normal vector.
  5. [B1] Equation of line OD.
  6. [M1] Substitutes into equation of plane.
  7. [A1]

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About this question

Topic
Vectors, A-Level Further Mathematics (syllabus 9231). Structured question, 10 marks.
Source
A-Level Further Mathematics, May/June 2022 Paper 1 Variant 2, question 2.

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