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

Engineering Mathematics - II - Vector Calculus - 2007
Page 37 of 72
x
g
f
g
x
f
i
x
g
f
i
g
x
f
i
x
g
)
f
.
( i
f
x
g
i
g
x
f
.
i
x
f
g)
.
( i
x
g
f
x
g
.
i
f
x
f
.
i
g
x
f
g 1
1
g
)
.
( f
g
div
f
f
g div
f
)
( g .
g
)
.
f
(
f
)
( g .
f
div
g
g
div
f
Question and answers
01. If
h
g,
,
f
are vectors functions of a scalar variable t. Prove that
dt
d h
x
g
x
f
h
x
dt
d g
x
f
h
x
g
x
dt
f
d
h
x
g
x
f
dt
d
Suggested answer:
h
x
g
dt
d
x
f
h
x
g
x
dt
f
d
h
x
g
x
f
dt
d
dt
d h
x
g
h
x
dt
d g
x
f
h
x
g
x
dt
f
d
dt
d h
x
g
fx
h
x
dt
d g
x
f
h
x
g
x
dt
f
d
02. If
k
t
j
sin t
i
cos t
g
2t k,
j
e
i
e
f
,
e
t
t
2t