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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)/(61))`

B

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

C

`sqrt((137)/(61))`

D

`sqrt((155)/(61)`

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,
`cos theta=(|2.2-1.1-1.6|)/(sqrt(4+1+36).sqrt(4+1+1))=(3)/(sqrt(246))`
`"Length of projection "=(AB) sin theta=sqrt6.sqrt(1-(9)/(246))=sqrt((237)/(41))" units."`
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