Find the equation of the plane containing line `(x+1)/(-3)=(y-3)/(2)=(z+2)/(1)` and point `(0, 7, -7)`.

Explanation

Let equation of the plane passing through the point `(0,7,-7) = 0"….."(1)`
Line passes through the poin t `(-1,3,-2)` . Therefore this point will be on the plane.
From eq. (1)
`-a-4b+5c=0"……"(2)`
The plane will be parallel to the line.
`:. -3a+2b+c=0"......"(3)`
Solving eqs. (2) and (3) by cross multiplication method.
`(a)/(-4-10) = (b)/(-15+1) = (c )/(-2-12)`
`a/(-4) = (b)/(-14) = c/(-14)`
`rArr a = b = c = k ("Say")`
Now from eq. (1)
`kx+k(y-7)+k(z+7)=0`
`rArr x+y+z=0`
Which is the required equation of the plane.