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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ii)<br />
Engineering Mathematics - II - <strong>Vector</strong> Calculus - 2007<br />
<br />
<br />
<br />
2 r<br />
div<br />
<br />
r<br />
2 <br />
<br />
Suggested answer:<br />
i) <br />
2<br />
r<br />
2<br />
<br />
<br />
2<br />
2<br />
2<br />
(r<br />
2 <br />
) (r<br />
2 <br />
) (r<br />
2<br />
)<br />
x<br />
2<br />
y<br />
2<br />
z<br />
2<br />
<br />
x y <br />
2r<br />
2r<br />
<br />
x<br />
r y<br />
r <br />
<br />
<br />
<br />
2r<br />
z <br />
z <br />
<br />
r <br />
= 2 + 2 + 2<br />
= 6<br />
ii)<br />
<br />
r 1 1<br />
div<br />
<br />
<br />
. r <br />
r<br />
2<br />
r<br />
2<br />
r<br />
2<br />
<br />
<br />
div r<br />
<br />
<br />
2 r 1<br />
.<br />
r (3)<br />
r<br />
3 r r<br />
2<br />
<br />
<br />
2 3 <br />
r<br />
2<br />
r<br />
2<br />
1<br />
<br />
r<br />
2<br />
40.<br />
3 Find the value of a if f(axy x) i(a 2)x j(1<br />
2 a )xz<br />
2<br />
<br />
k<br />
is irrotational.<br />
Suggested answer:<br />
Since<br />
<br />
f is irrotational<br />
Page 68 of 72
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