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
`!(x-0)/2=(y-0)/(-1)=(z-0)/5`
`=(-(0+0+0-3))/((2)^(2)+(-1)^(2)+(5)^(2))`
`!x/2=y/(-1)=z/5=3/30=1/10`
`thereforex/2=1/10,y/(-1)=1/10,z/5=1/10`
`!x=1/5,y=-1/10,z=1/2`