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 />
c i 3 j<br />
2 k at t = 1.<br />
Suggested answer:<br />
<br />
r (t<br />
3<br />
<br />
1) i t<br />
2<br />
j<br />
(t 5) k<br />
<br />
d r <br />
3t<br />
2<br />
i 2t j<br />
k<br />
dt<br />
<br />
d<br />
2<br />
r<br />
dt<br />
2<br />
<br />
6t i 2 j<br />
<br />
d r <br />
<br />
dt <br />
t1<br />
<br />
v 3 i 2 j<br />
k<br />
Now velocity along<br />
<br />
c is<br />
<br />
v c <br />
11<br />
14<br />
12<br />
<strong>Acceleration</strong> along c is a . c .<br />
14<br />
<br />
<br />
d d A d<br />
2<br />
A d A d<br />
3<br />
<br />
<br />
<br />
A <br />
10. Show that A, , A . x .<br />
dt<br />
<br />
dt dt<br />
2 <br />
dt dt<br />
3<br />
<br />
<br />
<br />
<br />
<br />
<br />
Suggested answer:<br />
d<br />
dt<br />
<br />
<br />
<br />
A,<br />
<br />
<br />
<br />
d A<br />
,<br />
dt<br />
<br />
d<br />
2<br />
A <br />
2 <br />
dt <br />
<br />
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d A<br />
,<br />
dt<br />
<br />
<br />
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d A<br />
,<br />
dt<br />
<br />
<br />
d<br />
2<br />
A <br />
<br />
A,<br />
dt<br />
2<br />
<br />
<br />
<br />
d<br />
2<br />
A<br />
,<br />
dt<br />
2<br />
<br />
<br />
d<br />
2<br />
A <br />
<br />
A,<br />
dt<br />
2<br />
<br />
<br />
<br />
d A<br />
,<br />
dt<br />
<br />
d<br />
3<br />
A <br />
3 <br />
dt <br />
<br />
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