The length of projection of the line segment joining the points `(1,0,-1) and (-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))`

Options

A. 2
B. `sqrt((271)/(53))`
C. `sqrt((472)/(31))`
D. `sqrt((474)/(35))`

Answer

d

Explanation

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