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 d f <br />
f . . f 0<br />
dt dt<br />
<br />
d f<br />
f .<br />
dt<br />
0<br />
7. If<br />
<br />
f<br />
has<br />
a<br />
fixed<br />
direction<br />
then<br />
<br />
f<br />
<br />
d f <br />
0<br />
dt<br />
Proof:<br />
Let<br />
<br />
f<br />
<br />
<br />
f e<br />
Now<br />
<br />
f <br />
<br />
d f<br />
dt<br />
<br />
f e <br />
d<br />
dt<br />
<br />
(f e)<br />
<br />
df d e <br />
f e e 0<br />
dt dt<br />
f<br />
df<br />
dt<br />
<br />
(e e)<br />
df <br />
f (0)<br />
dt<br />
<br />
0<br />
8.If<br />
<br />
f<br />
<br />
<br />
d f<br />
dt<br />
<br />
<br />
0<br />
then<br />
<br />
f<br />
has<br />
a<br />
fixed<br />
direction.<br />
Equation of a Space Curve<br />
Let P (x,y,z) be any point in space then its position vector is<br />
<br />
OP<br />
<br />
<br />
r<br />
<br />
<br />
x i<br />
<br />
y j<br />
<br />
<br />
z k<br />
If x = x(t), y = y(t) <strong>and</strong> z = z(t) are functions of a scalar variable<br />
t then<br />
<br />
r r (t)<br />
describes<br />
a<br />
curve<br />
in<br />
space<br />
called<br />
the<br />
space<br />
curve.<br />
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