Question

Does line (L) lie on plane P?
L: (x-2)/1 = (y+3)/-2 = (z-1)/1
P has equation 3x+y-z=2

a) find the equation of the plane that contains L that is perpendicular to P

b) find the equations for the line in P that is perpendicular to L and intersects it in (2, -3, 1)

Answer 1

So I've said U (3, 1, -1) is a normal vector to the plane
and that the directional vector of L is (1,-2,1)

then i've used U.V=0 to show the line is parallel to the plane
1*3 + 1*-2+1*1 = 0

I've shown point (2,-3,1) is shared therefore line lies on plane? now I'm a bit lost.

Answer 2

1*(3) + 1*(-2)+*(-1)*1 correction for U.V