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 />
<br />
[a, b , r ]<br />
In (1)<br />
<br />
div{( a x r )x(b x r )} [a, b , r ] 3[a, b , r ]<br />
<br />
[a, b , r ]<br />
28.<br />
<br />
If a<br />
<strong>and</strong><br />
<br />
b<br />
are vectors, prove that<br />
<br />
1<br />
1 <br />
a . {b . } {3( a, r )(b . r ) r<br />
2<br />
<br />
( a . b )}.<br />
r r<br />
5<br />
Suggested answer:<br />
<br />
<br />
1<br />
1<br />
r<br />
b . <br />
b . <br />
r <br />
r<br />
2<br />
r<br />
<br />
1 <br />
(b . r )<br />
r<br />
3<br />
<br />
<br />
1<br />
b . <br />
<br />
<br />
<br />
r <br />
1 1<br />
(b . r ) (b . r ) <br />
<br />
3<br />
3<br />
r<br />
r <br />
<br />
<br />
1 3 r<br />
[b ] (b . r ). <br />
r<br />
3<br />
r<br />
4<br />
r<br />
<br />
<br />
1<br />
b . <br />
<br />
<br />
<br />
r <br />
<br />
b 3(b . r ) <br />
r<br />
r<br />
3<br />
r<br />
5<br />
<br />
<br />
<br />
<br />
1<br />
b 3(b . r )<br />
a . b . <br />
a . . a . r<br />
<br />
r <br />
r<br />
3 r<br />
5<br />
<br />
Page 60 of 72
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