Find the co-ordinates of the foot of perpendicular and the length of perpendicular drawn from the point `(2,3,7)` to the plane `3x-y-z=7`.

Explanation

Plane:-`3x-y-z=7`


`Q(2,3,7)`


DR's of normal to the plane `(3,-1,-1)`


Let Point`P` be the foot of the perpendicular from `Q(2,3,7)` and DR'S `(3,-1,-1)`


`\frac{x-x}{a}=\frac{y-y_{1}}{b}=\frac{z-z}{c}`


`\frac{x-2}{3}=y \frac{-3}{-1}=\frac{z-7}{-1}=k(\text {say})`


`x=3 k+2 ; y=-k+3 ; z=-k+7`


`P(3 k+2,-k+3,-k+7)`


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