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 />
tangential component acceleration is<br />
<br />
a .v <br />
70<br />
29<br />
<br />
Normal component of acceleration |<br />
a ( a .v) v |<br />
<br />
<br />
82 i 36 j<br />
68 k<br />
29<br />
<br />
1<br />
29<br />
82<br />
2<br />
36<br />
2<br />
68<br />
2<br />
= 3.8774<br />
15. If is a function of r only, then prove that<br />
1 d<br />
d<br />
<br />
r r .<br />
r dr dr<br />
Suggested answer:<br />
We have<br />
r<br />
2<br />
<br />
r . r x<br />
2<br />
y<br />
2<br />
z<br />
2<br />
r<br />
x<br />
<br />
x<br />
r<br />
,<br />
r<br />
y<br />
<br />
y<br />
r<br />
,<br />
r<br />
z<br />
<br />
z<br />
r<br />
<br />
<br />
i<br />
x<br />
<br />
j<br />
y<br />
<br />
k<br />
z<br />
d<br />
i<br />
dr<br />
x<br />
r<br />
d<br />
j<br />
dr<br />
y<br />
r<br />
d<br />
k<br />
dr<br />
z<br />
r<br />
1 d<br />
<br />
(x i y j<br />
z k)<br />
r dr<br />
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