Sounds good to me. What do you get?Would I start off by finding the tangent to the surface, and then showing that the vector given by the curve is normal to the tangent plane?
1) Determine if the curve and surface do intersect at (1, 1, 1)!
2) Determine the tangent vector to the curve at that point.
3) Determine the normal vector to the plane at that point.
The curves intersects the surface at right angles at that point if and only if the tangent vector to the curve is a multiple of the normal vector to the plane.