A vector field E is characterized in spherical coordinate system by the following properties: (a) E points along R, (b) the magnitude of E is a function of only the distance from the origin, (c) E vanishes at the origin, and (d) V.E = 19, everywhere. Determine the field at (3,7/2,7) that satisfies the above properties. Answer: E = R

Find the curl of the vector field F (5y cos(r), 2r sin(y)). curl F =

A vector field is defined in spherical coordinates by F(r, 0, 0) = r² cos 0 e, + r sin sine. Enter an expression giving the divergence of this vector field in the box below (spell out greek letters, that is use theta for and use phi for $). V.F=

4. Assume A is a constant vector field and R = xi + yi + zk. (a) Simplify the expression (R. VR) · Ã+ V ·V × V × ((Ã × R) × (R × Ã)). (b) Assuming A the position vector of a point on the unit sphere centered at the origin, evaluate the above expression at R = A.