Hi there I was attempting a previous exam question on vector products but I was not sure it I had done it correctly. Could someone please look over my solution and help me out to part B.
Show that the line L:
lies on the Plane P, and find:
(a) the equation of the plane that contains L and is perpendicular to P.
(b) equations for the line P that is perpendicular to L and intersects it in (2,-3,1)
To show that the line lies on the plane:
I got the parametric form of L, giving x = t + 2, y = -2t -3 and z = t + 1
I then put this in the equation of the plane which gave me 2, so I said since LHS = RHS the line lies on the plane.
for part (a):
I did the vector product of the normal vector x direction vector of L:
which gave me (-1,-4,-3) and then I got the resulting plane equation as
x + 4y +3z = 17. Is this correct?