Distance of point `P(vecP)` from the plane `vecr.vecn=0` is

Options

A. `|vecp.vecn|`
B. `(|vecpxxvecn|)/(|vecn|)`
C. `(|vecp.vecn|)/(|vecn|)`
D. none of these

Answer

c

Explanation

Let `Q(vecq)` be the foot of altitude drawn from P to
the plane `vecr.vecn=0`. Then
`vecq-vecp=lamdavecnorvecq=vecp+lamdavecn`
Also `vecq.vecn=0implies(vecp+lamdavecn).=0`
or `lamda=-(vecp.vecn)/(|vecn|^(2))orvecq-vecp=-(vecp.vecn)/(|vecn|^(2))vecn`
Thus, required distance `=|vecq-vecp|=(|vecp.vecn|)/(|vecn|)=(|vecp.vecn|)`