Foot of perpendicular drawn from the origin to the plane `2x-3y+4z=29` is

Options

A. `(7,-1,3)`
B. `(5-1,4)`
C. `(5,-2,3)`
D. `(2,-3,4)`

Answer

D

Explanation

Since, PQ is perpendicular to plane
`2x-3y+4z=29`. Hence, DR's of PQ will be (2,-3,4).
Equation of line PQ will be
`(x-0)/(2)=(y-0)/(-3)=(z-0)/(4)=lamda`
Coordinates of Q will be `(2lamda,-3lamda,4lamda)`.
`because` Q lies on plane, so it satisfies
`4lamda=9lamda+16=29rArrlamda=1`
`:.` Coordinates of Q are `(2,-3,4)`.