phy302 from 8 through to 10 please

8. In this exercise, use the following vectors: 382 4142 r = xx + yy + zz, V = yzx + czy + ryz, U = Ity+ z2 (12+ 2)3/2 (12 + 12) 3/2 . (a) Compute (V . V)r. (b) Show that both Vx V 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. 9. Prove that Vx (1Vy) =0, where y is a scalar function. 10. If A is a constant vector, prove that Vx(A x r) = 2A, where r is the position vector given in Exercise 8 above