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 />
<br />
d A d<br />
3<br />
A <br />
0 0 A,<br />
,<br />
dt 3 <br />
dt <br />
<br />
<br />
<br />
<br />
11. If R A e<br />
nt<br />
B e<br />
nt<br />
, where A <strong>and</strong> B are cons tan t vectors<br />
<br />
d<br />
2<br />
R <br />
then show that n<br />
2<br />
R .<br />
dt<br />
2<br />
Suggested answer:<br />
<br />
d R<br />
dt<br />
<br />
ne<br />
nt<br />
A ne<br />
nt<br />
B<br />
<br />
d<br />
2<br />
R<br />
dt<br />
2<br />
<br />
n<br />
2<br />
e<br />
nt<br />
A n<br />
2<br />
e<br />
nt<br />
B<br />
<br />
n 2 R<br />
<br />
12. Find unit vector normal to the curve 4 sin t i 4 cos t j<br />
3t k .<br />
Suggested answer:<br />
We have<br />
<br />
r 4 sin t i 4 cos t j<br />
3t k<br />
<br />
d r<br />
dt<br />
<br />
4 cos t i 4 sin t j<br />
3k<br />
<br />
d r<br />
dt<br />
5<br />
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