1. (20%) Calculate the divergence (.v) for the following vector fields:

(a) v = (x )x2 1 + (x3

2

3x1) 2 + 4x2 3

(b) v = (3x + 2x3) 1 + (x13 x2

2) 2 + (x3 7x1) 3

(c) v = 5ex1x2

1 - 8ex2x3 2

(d) v = 2x13 1 - x1 sin(x1 x2) 2

In each case, 1, 2 and 3 are unit vectors in x1, x2, and x3 direction respectively

(20\%) Calculate the divergence ( .y) for the following vector fields: (a) v=(x2)x21+(x323x1)2+4x23 (b) v=(3x1+2x3)1+(x13x22)2+(x37x1)3 (c) v=5ex218e232 (d) v=2x131x1sin(x1x2)2 In each case, 1,2 and 3 are unit vectors in x1,x2, and x3 direction respectively