let `Q` be the foot of perpendicular from the origin to the plane `4x-3y+z+13=0` and `R` be a point `(-1,1,-6)` on the plane then length `QR` is

Options

A. `sqrt(14)`
B. `sqrt((19)/(2))`
C. `3sqrt((7)/(2))`
D. `(3)/(sqrt(2))`

Answer

C

Explanation

The foot of perpendicular Q(x,y,z) from O(0,0,0) is
`(x-0)/(4)=(y-0)/(-3)=(z-0)/(1)`
`=-({4(0)-3(0)+1(0)+13})/(4^(1)+3^(2)+1^(2))`
`rArr" "(x)/(4)=(y)/(-3)=(z)/(1)=(-13)/(26)=-(1)/(2)`
`x=-2,y=(3)/(2),z=-(1)/(2)`
`:." "Q(-2,(3)/(2),-(1)/(2))`
`:.` The length QR `=sqrt((-1+2)^(2)+(1-(3)/(2))^(2)+(-6+(1)/(2))^(2))`
`=sqrt(1+(1)/(4)+(121)/(4))=(sqrt(126))/(2)=3sqrt((7)/(2))`