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

Engineering Mathematics - II - Vector Calculus - 2007
Page 16 of 72
From (1), (2) and (3)
f
)
( g .
g
)
.
( f
f
Curl
g
g
Curl
f
g)
.
( f
Note:
f
)
.
2( f
f
Curl
f
2
)
f
.
( f
then
g
f
If
f
)
.
( f
f
Curl
f
)
f
.
( f
grad
2
1
or
(iv) Curl of a vector product
then
fields
vector
are
g
and
f
If
g
)
.
( f
f
)
( g .
f
g div
g
div
f
g)
( f
Curl
Proof:
g)
( f
x
i
g)
( f
Curl
x
g
f
g
x
f
i
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
Integration of Vector functions
a
be
C
and
space
in
R
region
a
over
defined
field
vector
a
be
f
Let