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

Let the direction ratios of the plane =(a , b , c)

Direction ratio of given line (-3,2,1) 

As,

The plane contain the line= -3a+2b+c=0 ...................(i)

Now,

Equation of plane 

a(x-0) +b(y -7) +c[z-(-7)] =0 

a(x-0) +b(y -7) +c(z+7) =0 

The point (-1,3,-2) satisfy the equation of plane.

⇒a(-1-0) +b(3-7) +c(-2+7)=0

⇒-a-4b+5c=0

⇒ a+4b-5c=0...................(ii)

On Solving (i) and (ii), we get,

⇒ a=14 

 b=14 

and

 c=14

Thus, the equation of plane

⇒14(x-0) + 14(y-7) +14(z+7)=0

⇒x+y+z=0