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

Engineering Mathematics - II - Vector Calculus - 2007
Suggested answer:
F is irrotational if
Curl F 0
i j k
CurlF
0
x y z
x 2y az bx 3y z 4x cy 2z
c 1 0, 4 a 0, b 2 0
a 4,b 2, c 1
38. If and
are scalar fields prove that
i) div{ }
2
.
ii)
2
( )
2
2
2.
Suggested answer:
i) div( )
.
div( )
.
2
...(1)
ii) similarly
div( ) .
2
...(2)
adding (1) and (2)
div( )
div( )
2
2
2.
...(3)
Also div(
) div( ) div( ( ))
2
( )
2
( )
2
2
2.
39. Evaluate
i)
2 r
2
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