2x - 3y - 3z = 8
We've been given the normal vector to the plane <2, -3, -3> and a point within the plane (1, -5, 3). In general if you've been given both the normal vector <a,b,c> and a point (e,f,g) within the plane, the expression for the plane will be: ax + by + cz = d
and you can compute d by:
d = ae + bf + cg
So let's calculate d:
d = ae + bf + cg
d = 2*1 + -3*-5 + -3*3
d = 2 + 15 + -9
d = 8
And the equation for the plane is 2x - 3y - 3z = 8