The co-ordinates of the foot of perpendicular drawn from origin to the plane 2x-y+5z-3=0 are

Options

A. `((2)/(sqrt(30)),(-1)/(sqrt(30)),(5)/(sqrt(30)))`
B. `(2,-1,5)`
C. `((2)/(3),(-1)/(3),(5)/(3))`
D. `((1)/(5),(-1)/(10),(1)/(2))`

Answer

D

Explanation

Given equation of plane is `2x-y+5z-3=0`
`therefore` Foot of perpendicular drawn from origin to the given plane
`implies(x-0)/(2)=(y-0)/(1)=(z-0)/(5)`
`=(-(0+0+0-3))/((2)^(2)+(-1)^(2)+(5)^(2))`
`implies(x)/(2)=(y)/(-1)=(z)/(5)=(3)/(30)=(1)/(10)`
`implies(x)/(2)=(1)/(10),(y)/(-1)=(1)/(10),(z)/(5)=(1)/(10)`
`impliesx=(1)/(5),y=-(1)/(10),z=(1)/(2)`