Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
f g i (f2
g3
g2
f3)
d
dt
( f g)
d
dt
i (f2
g3
g2
f3)
d f
i
2
dt
g3
f2
dg3
dt
dg2
dt
f3
g2
df3
dt
d f
i
2
dt
dg
g
2
3
dt
f3
i
f2
dg3
dt
g2
df3
dt
d f
dt
g
f
d g
dt
5.
d
dt
f , g, h
d
f
,
dt
g, h
f
,
d g
d h
,h f , g ,
dt
dt
Proof:
d
dt
f ,
g,
h
d
dt
f
g .
h
d
dt
f
g .
h
f
g .
d h
dt
d f
dt
g
.
h
f
d g
.
dt
h
f g .
d h
dt
d
f
,
dt
g , h
d g
f , , h
dt
f ,
g,
d h
dt
d f
6. If | f | cons tan t then f . 0
dt
Proof:
Let | f |
C
| f | a
2
where a is constant
f .
f
cons tan t
d
dt
f .
f
0
Page 4 of 72