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

Engineering Mathematics - II - Vector Calculus - 2007
f
g i
x
f
g . i
x
g . i
f
x
i
f
g .
x
g .
f
g
Curl
f
( g . )
g
i
f
g .
x
...(2)
Similarly
f
curl g
From (1), (2) and (3)
Note:
( f . g)
( f . )
g
f Curl
g
g
i f .
x
g Curl
f
...(3)
( f . )
g ( g . )
f
If
f
g
then
( f . f )
2 f
Curl
f 2( f . )
f
or
1
grad ( f . f )
2
f
Curl
f
( f . )
f
(iv) Curl of a vector product
If f
and
g
are
vector
fields
then
Curl ( f
g)
f div
g g div f ( g . )
f ( f . )
g
Proof:
Curl ( f g)
i
x
( f g)
i
f
x
g
f
g
x
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