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The length of projection of the line ...

The length of projection of the line segment joining the points `(1,0,-1)a n d(-1,2,2)` on the plane `x+3y-5z=6` is equal to a. `2` b. `sqrt((271)/(53))` c. `sqrt((472)/(31))` d. `sqrt((474)/(35))`

Text Solution

Verified by Experts

The correct Answer is:
`3`
Let `A(1, 0, -1), B(-1, 2, 2)`
Direction ratios of `AB` are `(2, -2, -3)`
Let `theta` be the angle between the line and normal to plane , then
`" "costheta= (|2.1+ 3(-2)-5(-3)|)/(sqrt(1+9+25)sqrt(4+4+9))`
`" "= (11)/(sqrt(17)sqrt(35))= (11)/(sqrt(595))`
Length of projection
`" "=(AB) sin theta`
`" "= sqrt((2)^(2)+ (2)^(2)+ (3)^(2))xxsqrt(1- (121)/(595))`
`" "= sqrt((474)/(35))` units
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