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

Engineering Mathematics - II - Vector Calculus - 2007
c x i y j
z k
i)
div[( a . r ) b ] ( a . r ). b a . r div b
a . b ( a . r )(0)
a . b
ii) we have a x( r x b ) ( a . b ) r ( a . r ) b
div{ a x( r x b )} div{( a . b ) r } div{( a . r ) b}
( a . b )div r ( a x r ). b ( a . r )div b
( a . b )3 a . b ( a r )0
2( a . b )
iii)Let
a x r p
( a x r )x(b x r ) p x(b x r )
(p . r ) b (p . b ) r
{( a x r ). r } b {( a x r ). b} r
2( a . b )
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