The length of projection, of the line segment joining the points `(1, -1 , 0) and (-1, 0, 1)` to the plane `2x + y + 6z = 1`,is equal to

Options

A. `sqrt((255)/(41))`
B. `sqrt((237)/(41))`
C. `sqrt((137)/(41))`
D. `sqrt((155)/(41))`

Answer

B

Explanation

Let `A-=(1,-1,0),B-=(-1,0,1)`
`therefore` direction ratios of segment AB are (2,-1,-1). If `theta` be the acute angle between segment AB and normal to plane,
`costheta=(|2.2-1.1-1.6|)/(sqrt(4+1+36)*sqrt(4+1+1))=(3)/(sqrt(246))`
Length of projection `=(AB)sintheta=sqrt(6)*sqrt(1-(9)/(246))=sqrt((237)/(41))` units.