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

Engineering Mathematics - II - Vector Calculus - 2007
Page 33 of 72
i
f
z
f
y
2
3
f
f
curl
)
f
(
Curl
(iv)
0
)
(
Curl
Proof:
i
y
z
z
y
)
(
Curl
0
(v). 0
)
f
(Curl
div
then
field
vector
a
is
f
If
Proof:
k
y
f
x
f
i
x
f
z
f
i
z
f
y
f
f
Curl
1
2
3
1
2
3
y
f
x
f
x
x
f
z
f
z
z
f
y
f
x
f )
(curl
div
1
2
3
1
2
3
y
z
f
x
z
f
x
y
f
z
y
f
z
x
f
y
x
f 1
2
2
2
3
2
1
2
2
2
3
2
= 0
Some important Identities
(i) Divergence of a vector product:
then
fields
vector
are
g
and
f
If
g
curl
.
f
f
g .curl
g)
( f
div
Proof:
k
f
j
f
i
f
f
Let 3
2
1
k
g
j
g
i
g
g 3
2
1
k
)
g
f
g
(f
j
)
g
f
g
(f
i
)
f
g
g
(f
g
f 1
2
2
1
3
1
1
3
3
2
3
2
2
3
3
2 g
f
g
f
x
g)
div (f