1

8. In this exercise, use the following vectors: r = xx + yy+ zz, V = yzx + xzy+xyz, 202 + 32 + 2 2 2 U = (202 + 22) 3/2" Z (2 2 + 2 2) 3/2 (a) Compute (V . V) r. (b) Show that both VxV and VXU are zero, first by direct computation, and then by finding scalar functions whose gradients equal V and U. Caution: Think a bit about how to simplify the computation of VXU before starting, to save yourself considerable trouble! (c) Compute (U. V) V and (V. V) U, and from a convenient identity, compute V (U . V). (d) Write V and U in circular cylindrical coordinates