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 />
d f <br />
i) f x n( a x b)<br />
dt<br />
ii)<br />
<br />
d<br />
2<br />
f<br />
dt<br />
2<br />
<br />
n<br />
2<br />
f<br />
iii)<br />
<br />
<br />
<br />
f ,<br />
<br />
<br />
<br />
d f d<br />
2<br />
f <br />
, 0<br />
dt dt<br />
2 <br />
<br />
<br />
Suggested answer:<br />
Given<br />
<br />
f cos nt a sinnt b<br />
<br />
d f<br />
i) f x<br />
dt<br />
<br />
d f<br />
<br />
<br />
n sinnt a n cos nt b<br />
dt<br />
<br />
<br />
<br />
(cos nt a sinnt b )x( n sinnt a n cos nt b )<br />
<br />
<br />
n cos<br />
2<br />
nt( a x b ) n sin<br />
2<br />
t(b x a)<br />
<br />
n( a x b )<br />
<br />
d<br />
2<br />
f<br />
ii)<br />
dt<br />
2<br />
<br />
<br />
n<br />
2<br />
cos nt a n<br />
2<br />
sinnt b<br />
<br />
<br />
f<br />
<br />
<br />
<br />
iii) f ,<br />
<br />
<br />
<br />
d f<br />
,<br />
dt<br />
n 2 0<br />
<br />
<br />
d<br />
2<br />
f <br />
d f <br />
f , , n<br />
2 <br />
f<br />
dt<br />
2 <br />
dt<br />
<br />
<br />
<br />
<br />
<br />
<br />
09. A particle moves along the curve x = t 3 + 1, y = t 2 , z = t + 5 where t is the<br />
time. Find the components of velocity <strong>and</strong> acceleration along the vector<br />
Page 43 of 72
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