If P be the point `(2,6, 3)` then the equation of the plane through P, at right angles to OP, where 'O' is the origin is

Options

A. `2x+6y+3z=7`
B. `2x-6y+3z=7`
C. `2x+6y-3z=49`
D. `2x+6y+3z=49`

Answer

D

Explanation

distance of point P(2,6,3) from origin
`OP sqrt((0-2)^(2)+(0-6)^(2)+(0-3)^(2))`
=7
DR's of `OP=2-0,6-0`
`3-0=2,6,3`
` :.` DC's of OP are `(2)/(7),(6)/(7),(3)/(7)`
`:.` Equation of plane in normal form is
`Ix+_my+nz=p`
`rArr (2)/(7)x+(6)/(7)y+(3)/(7)z=07`
`rArr 2x+6y+3z=49`