Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...
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Engineering Mathematics - II - <strong>Vector</strong> Calculus - 2007<br />
1(1) 1(1) (1)<br />
. n <br />
3<br />
3<br />
<br />
<br />
<br />
21. If F (x<br />
3<br />
y<br />
3<br />
z<br />
3<br />
3xyz) find div F <strong>and</strong> curl F .<br />
Suggested answer:<br />
<br />
F (3x<br />
2<br />
<br />
3yz) i<br />
(3y<br />
2<br />
<br />
3xz) j<br />
(3z<br />
2<br />
<br />
3xy) k<br />
<br />
div F 6x 6y 6z<br />
<br />
i j k<br />
<br />
Curl F <br />
x y z<br />
3x<br />
2<br />
3yz 3y<br />
2<br />
3xz 3z<br />
2<br />
3xy<br />
<br />
<br />
<br />
i(<br />
3x<br />
3x) j( 3y<br />
3y) k( 3z<br />
3z)<br />
<br />
0<br />
22. If<br />
<br />
is a constant vector <strong>and</strong><br />
<br />
v x r<br />
then show that<br />
<br />
div v 0.<br />
Suggested answer:<br />
Let<br />
<br />
r x i y j<br />
z k<br />
<br />
v x r<br />
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