Question
The co-ordinates of a point P are (a, b, c) where a, b, c > 0. If the perpendicular distance of P from XY-plane is equal to half the sum of its perpendicular distances from ZX-plane and YZ-plane, find a relation between a, b and c.
Solution
Perpendicular distance of point P from XY-plane = 
(∵ c>0)
Similarly, the perpendicular distances of P(a, b, c) from ZX-plane and YZ-plane are b and a respectively. According to the question, we have
∴ a + b - 2c = 0
Which is the required relation between a, b and c
