34

Solution

(a) Rewrite as2214 yxz 14222 zyx

Thus, we obtain222),,( zyxzyx

Then, )(2222 kjikji zyxzyx

At the point (1,3,2),

The unit normal vector is14

23

kjin

14223)1(2 222 and)23(2 kji

35

(b) Rewrite as

Thus, we obtain

Then,

At the point (1,0,1),

The unit normal vector is6

2

kjin

6211 222 and

23),,( zyxezyx y

kji zyxee yy 2)3( 2

23 zyxey 023 zyxey

kjikji 2)1(2])0(31[ 200 ee

36

Divergence of Vector Fields

The divergence is an operator that

measures the magnitude of a vector field's

source or sink at a given point

The divergence of a vector field is a scalar

(x,y,z)V (x dx,y,z)V

x x+dx