Question

1. (This tests Corollary 1 on page 35 of your book.) A triangular prism is placed as shown in the figure. The triangular face at the bottom has its vertices at (0, 0, 0), (1,0,0) and (0,1,0. The triangular face at the top has its vertices at (0, 0,1), (1, 0, 1) and (0, 1, 1). Consider the vector field a) Calculate V x v.da over the red rectangle, with the normal to the surface pointing away from the origin b) Repeat the same calculation, but summing over the remaining four surfaces of the prism, and show that your result is the same. Be careful about the orientation of each of the surfaces c) Show that the divergence theorem Eq.(1.56) implies that V (Vx v)dxdydz integrated over the prism is zero. Verify that the integrand itself is zero.

Answer 1