1.

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

Answer» 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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