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| PAGE: 1121 | SET: Exercises | PROBLEM: 3 |
If 
is a vector field on 
and the partial derivatives of P , Q and R all are exists, then the curl of F is
, or
And the divergence of F is 
.
(a)
The vector field is 
.
Compare 
with 
.
and 
.
Find the curl of the vector field F.
The curl of the vector field F is 
(b)
Consider 
.
Apply partial derivative on each side with respect to x.
Consider 
.
Apply partial derivative on each side with respect to y.
Consider 
.
Apply partial derivative on each side with respect to z.
Find the divergence of the function.
Substitute corresponding values.
The divergence of the vector field F is 
(a) The curl of the vector field F is 
.
(b) The divergence of the vector field F is 
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