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The length of projection, of the line se...

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

A

`sqrt((255)/(41))`

B

`sqrt((237)/(41))`

C

`sqrt((137)/(41))`

D

`sqrt((155)/(41))`

Text Solution

Verified by Experts

The correct Answer is:
B
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.
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