1. With your unit vector the object leaves the surface of the sphere.

2. All vectors which describethe direction the object is "looking at"form a plane (the tangent plane at P with the vector as it's normal vector. Let be the stationary vector pointing at an arbitrary point in the tangent plane and let be the staionary vector pointing at P and since you know the coordinates of P the equation of the tangent plane in P would be:

and