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 />
r x i y j<br />
z k<br />
<br />
<br />
i j k<br />
i)<br />
a x r a1<br />
a2<br />
a3<br />
x y z<br />
<br />
<br />
<br />
( a2z<br />
a3y)<br />
i (a3x<br />
a1z)<br />
j<br />
(a1y<br />
a2x)<br />
k<br />
<br />
<br />
<br />
div( a x r ) (a2z<br />
a3y)<br />
(a3x<br />
a1z)<br />
(a1y<br />
a2x)<br />
0<br />
x<br />
y<br />
z<br />
<br />
ii) r x( r x a) ( r . a) r ( r . r ) a<br />
<br />
div( r x( r x a)) ( r . a). r ( r . a)div r div(r<br />
2 <br />
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a)<br />
<br />
a . r ( r . a)3 a . r<br />
2<br />
<br />
r<br />
2<br />
div a<br />
<br />
a . r 3( a . r ) a{2r<br />
x<br />
r<br />
<br />
i <br />
y z <br />
2r j<br />
2r k}<br />
r r<br />
<br />
a . r 3( a . r ) 2( a . r )<br />
<br />
2( a . r )<br />
<br />
<br />
iii) div{r<br />
n<br />
( a x r )} r<br />
n<br />
.( a x r ) r<br />
n<br />
div( a x r )<br />
<br />
r <br />
nr<br />
n1<br />
.( a x r ) r<br />
n<br />
div( a x r )<br />
r<br />
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