You did not write "just del". You wrote del-dot. The dot was wrong. You can write del f or you can write grad f. Same thing. (But del-dot-F is OK whereas del F or grad F are not.)so what you are saying is that instead of just del I should have used del f for notation?
(∂f/∂x)x+(∂f/∂y)y+(∂f/∂z)z (where x, y, and z should be x(hat), y(hat), and z(hat))
Yes, ∂(-2xz)/∂y = 0.so if I am right which I probably am not then (a) 6yUx+(-0)+zUz the reason I put 0 is the the partial derivative of -2xz with respect to y is 0 correct since there is no y term.
Problem here.for V3 ((-2/r^2)cos(phi))i-((2sin(phi))/(r^2sin(theta)))k
Correct, except again you don't use i j k as unit vectors for spherical coordinates. Use 1r, 1φ and 1θ.for V3 ((-2/r^2)cos(phi))i-((2sin(phi))/(r^2sin(theta)))k