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.
A second plane p is parallel to m and nearer to O. The perpendicular distance between the planes is 1.
(ii) Find the equation of p, giving your answer in the form ax + by + cz = d.
Solution:
Reference: PYQ - May/Jun 2017 Paper 31 Q6
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