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 />
iii)Let a x r p<br />
<br />
( a x r )x(b x r ) p x(b x r )<br />
<br />
(p . r ) b (p . b ) r<br />
<br />
{( a x r ). r } b {( a x r ). b} r<br />
<br />
0 [ a, r , b ] r<br />
<br />
( a x r )x(b x r ) [a,<br />
<br />
b ,<br />
<br />
r ] r<br />
<br />
div{( a x r )x(b x r )} [a,<br />
b , r ]. r [a, b , r ]div r<br />
<br />
r . [a,<br />
b ,<br />
<br />
r ] [a, b , r ](3)<br />
...(1)<br />
<br />
a1<br />
a2<br />
a3<br />
[ a, b , r ] b1<br />
b2<br />
b3<br />
x y z<br />
a1(b<br />
2z<br />
b3y)<br />
a2(b1<br />
z b3x)<br />
a3(b1<br />
y b2x)<br />
<br />
<br />
<br />
<br />
[ a, b , r ] (a2b3<br />
a3b2<br />
) i ( a1b<br />
3 a3b1<br />
) j<br />
(a1b<br />
2 a2b1<br />
) k<br />
<br />
a x b<br />
<br />
Now r . [a,<br />
b , r ] r .( a x b )<br />
( a2b3<br />
a3b2<br />
)x (a3b1<br />
a1b<br />
3)y<br />
(a1b<br />
2 a2b1)z<br />
Page 59 of 72
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