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 />
Suggested answer:<br />
<br />
<br />
<br />
<br />
r (t<br />
2<br />
1) i (4t 3) j<br />
(2t<br />
2<br />
6t) k<br />
<br />
d r<br />
dt<br />
<br />
<br />
2t i 4 j<br />
(4t 6) k<br />
<br />
t <br />
<br />
<br />
2t i 4 j<br />
(4t 6)k<br />
4t<br />
2<br />
16 16t<br />
2<br />
36 48t<br />
<br />
<br />
<br />
2t i 4 j<br />
(4t 6)k<br />
20t<br />
2<br />
48t 52<br />
<br />
t t1<br />
<br />
<br />
2 i 4 j<br />
2 k<br />
24<br />
<br />
a<br />
(say)<br />
<br />
t t2<br />
<br />
<br />
4 i 4 j<br />
2 k<br />
36<br />
<br />
2 2 2 <br />
i j<br />
k b (say)<br />
3 3 3<br />
Let be the angle between<br />
<br />
a<br />
<br />
<strong>and</strong> b<br />
<br />
<br />
<br />
a . b<br />
cos 1 <br />
<br />
<br />
|<br />
a || b | <br />
<br />
<br />
5<br />
cos 1 <br />
3<br />
6 <br />
08. If<br />
<br />
f cosnt <br />
sinnt<br />
<br />
<br />
where n is a constant scalar <strong>and</strong><br />
<br />
<strong>and</strong> <br />
are<br />
constant vectors prove that<br />
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