Question

find the equation of plane passing through point(0,7,-7) and containing line x+1/-3=y-3/2=z+2/1

Answer 1

I assume you mean
(x+1)/-3 = (y-3)/2 = (z+2)/1 , the brackets are essential
so we know (-1,3,-2) is a point on the plane and we also have a direction vector of [-3,2,1]
using (0,7,-7) we can find a second direction vector which would be
[1,4,-5]
a normal to [-3,2,1] and [1,4,-5] is [-14, -14 , -14]
or reduced to [1,1,1]

So the equation of the plane is
x + y + z = c, but -1,3,-2) lies on it
-1 + 3 - 2 = c = 0

equation of plane:
x+y+z = 0