>>12130419question 2: start by evaluating the vector field at the point P by substituting the t, phi, theta values. Then, the point P's location is given in spherical coordinates you can immediately tell that P lies on the surface of the sphere (that might be obvious from the wording too, but I wouldn't know, I'm ESL). This means that the perpendicular vector component is just the r component of F (and zero on the other 2 components), and the parallel component is just the theta and phi components, and zero on r.
question 3: I can't be bothered to type. Literally just look up the divergence theorem, calculate the 2 integrals, see that the result is the same.
