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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t <br />
<br />
d r<br />
dt<br />
<br />
d r<br />
dt<br />
Engineering Mathematics - II - <strong>Vector</strong> Calculus - 2007<br />
<br />
<br />
4 cos t i 4 sin t j<br />
3k<br />
5<br />
<br />
d t<br />
ds<br />
<br />
<br />
d t dt <br />
<br />
dt ds <br />
<br />
d t/ dt<br />
ds / dt<br />
<br />
also<br />
ds d r<br />
<br />
dt dt<br />
5<br />
<br />
d t<br />
<br />
ds<br />
<br />
1<br />
25<br />
<br />
( 4 sin t i 4 cos t j)<br />
<strong>and</strong><br />
<br />
N <br />
<br />
4<br />
(sin t<br />
25<br />
<br />
i cos t j)<br />
16 /(25)<br />
2 <br />
<br />
<br />
(sin t i cos j)<br />
13. Find the unit normal vector to the curve x = 3 cost, y = 3sint, x = 4t.<br />
Suggested answer:<br />
We have<br />
<br />
r 3 cos t i 3 sin t j<br />
4t k<br />
<br />
d r<br />
v <br />
dt<br />
<br />
| v | 5<br />
<br />
3 sin t i 3 cos t j<br />
4 k<br />
(tan gent vector)<br />
Page 46 of 72
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