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 />
i j k<br />
<br />
x(<br />
x<br />
F ) <br />
x<br />
y<br />
z<br />
2z 2x 0 2z x<br />
2<br />
<br />
(2x 2) j<br />
31. Find the directional derivative of<br />
x<br />
2<br />
yz 4xz<br />
2<br />
at (1, -2, -1)<br />
<br />
in the direction 2 i j<br />
2 k .<br />
Suggested answer:<br />
<br />
<br />
<br />
(2xyz 4z<br />
2<br />
) i x<br />
2<br />
z j<br />
(x<br />
2<br />
y 8xz) k<br />
<br />
at<br />
(1,<br />
2,<br />
<br />
1)is 8 i j<br />
10 k<br />
Let<br />
<br />
c 2 i j<br />
2 k<br />
Directional derivative in the direction of<br />
<br />
c<br />
is<br />
<br />
(2 i j<br />
2 k)<br />
. c (8 i j<br />
10 k).<br />
3<br />
<br />
1<br />
(16<br />
3<br />
1 20)<br />
37<br />
<br />
3<br />
32. Find the directional derivative of 4xz<br />
3 3x<br />
2<br />
y<br />
2<br />
z at (2, -1, 2)<br />
<br />
in the direction of 2 i 3 j<br />
6 k .<br />
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