If the perpendicular distance of a point `A,` other than the origin from the plane `x + y + z = p` is equal to the distance of the plane from the origin, then the coordinates of `p` are (A) `(p,2p,0)` (B) `(0,2p,-p)` (C) `(2p,p,-p)` (D) `(2p,-p,2p)`

Options

A. `(p,2p,0)`
B. `(0,2p,-p)`
C. `(2p,p,-p)`
D. `(2p,-p,2p)`

Answer

C

Explanation

The perpendicular distance of the origin (0,0,0) from the plane x+y+z=p is
`|-p/sqrt(1+1+1)|=|p|/sqrt(3)`
If the coordinates of P are (x,y,z) then we must have `|(x+y+z-p)/sqrt(3)|=|p|/sqrt(3)`
`rArr |x+y+z-p|=|p|`
Which is satisfied by (c).