Question

If the perpendicular distance of a point 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 the point are

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

Answer 1

The correct option is C (2p, p, -p)

The perpendicular distance of the origin (0, 0, 0) from the plane x + y + z = p is $\left|\frac{-p}{\sqrt{1+1+1}}\right|=\frac{|p|}{\sqrt{3}}$
If the coordinates of P are (x, y, z), then we must have
$\left|\frac{x+y+z-p}{\sqrt{3}}\right|=\frac{|p|}{\sqrt{3}}\Rightarrow |x+y+z-p|=|p|$
Which is satisfied by (c)