A-LevelMathematicsVectors9709/31 · May/June 2017 · Q68 Marks
The plane with equation 2x + 2y – z = 5 is denoted by m. Relative to the origin O, the points A and B have coordinates (3, 4, 0) and (−1, 0, 2) respectively.
- (i)Show that the plane m bisects AB at right angles.[5]
- (ii)A second plane p is parallel to m and nearer to O. The perpendicular distance between the planes is 1. Find the equation of p, giving your answer in the form ax + by + cz = d.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- State or obtain coordinates (1, 2, 1) for the mid-point of AB B1
- Verify that the midpoint lies on m B1
- State or imply a correct normal vector to the plane, e.g. 2i + 2j - k B1
- State or imply a direction vector for the segment AB, e.g. –4i – 4j + 2k B1
- Confirm that m is perpendicular to AB B1
- State or imply that the perpendicular distance of m from the origin is √5, or unsimplified equivalent B1
- State or imply that p has an equation of the form 2x + 2y - z = k B1
- Obtain answer 2x + 2y - z = 2 B1
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