Two vector fields are given by F= (-3y, 3x, 0) and G=Vg , where g(x, y, z)=xy (2x + y).Assume uv w are the last three digits of your student

number. For example, if your student number isC1700123, then u =1, v=2 and w =3. (a) Evaluate the vector field G and calculate F and G at position vector(4,v, w). \text { (b) Evaluate the scalar fields } \underline{\nabla} \Pi \underline{F} \text { and } \underline{\nabla} \cap \underline{G} \text { and calculate them at }(u, v, w) \text { . } \text { Evaluate the vector fields } \underline{\nabla} \times \underline{F} \text { and } \underline{\nabla} \times \underline{G} \text { and calculate them at }(u, v, w) If L is the square loop joining the points (0,0,0), (w,0,0), (w, w,0),(0, w,0), calculate theline integrals If L is the square loop joining the points (0,0,0), (w,0,0), (w, w,0), (0, w,0), calculate the line integrals \oint_{L} \underline{F} \cdot \underline{d} \ell, \oint_{L} \underline{G} \cdot \underline{d \ell} )If S is the surface of a cube, of side w, centre d at the origin with its faces parallel to the x, y and z axes, calculate the following surface integrals, i.e. the fluxes of F and G through S \oint_{S} \underline{F} \cdot \underline{d S}, \oint_{S} \underline{G} \cdot \underline{d S}