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 />
1 3 r <br />
(0) x<br />
r<br />
r<br />
3 r<br />
4 r <br />
<br />
<br />
0 0<br />
<br />
0<br />
42. If<br />
<br />
a is a constant vector prove the following<br />
i)<br />
<br />
<br />
<br />
<br />
Curl( a . r ) a 0<br />
<br />
<br />
ii)Curl{ r x( a x r )} 3( r x a)<br />
<br />
<br />
iii)Curl{r<br />
n<br />
( a x r )} (n 2)r<br />
n<br />
a nr<br />
n2<br />
( r . a) r<br />
Suggested answer:<br />
<br />
i)Curl{( a . r ) a} ( a . r )Curl a ( a . r )x a<br />
<br />
( a . r ) 0 a x a ( a . r ) a<br />
<br />
0 0<br />
<br />
0<br />
<br />
<br />
ii) Curl{ r x( a x r )} Curl{( r . r ) a ( r . a) r }<br />
<br />
<br />
Curl{( r . r ) a} Curl{( r . a) r }<br />
<br />
( r . r )Curl a ( r . r )x a ( r . a)x r<br />
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