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
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))`
A. 2
B. `sqrt((271)/(53))`
C. `sqrt((472)/(31))`
D. `sqrt((474)/(35))`
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1 Answers
Correct Answer - d
Let A(1,0,-1), B(-1,2,2) Direction rations of segment AB are `lt2,-2,-3gt`
`becausecostheta=(|2xx1+3(-2)-5(-3)|)/(sqrt(1+9+25)sqrt4+4+9)`
`=(11)/(sqrt17sqrt35)=(11)/sqrt595`
Length of projection `=(AB)sintheta`
`=sqrt((2)^(2)+(2)^(2)+(3)^(2))xxsqrt((474)/(35))` units
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