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Question

* The line integral V.dr of the vector V=2xyz^i+x2z^j+x2y^k from the origin to the point (1, 1, 1)

A
is 1
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B
is zero
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C
is -1
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D
can not be determined without specifing the path
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Solution

The correct option is A is 1
V.dr=(2xyzdx+x2zdy+x2ydz)
=(1,1,1)(0,0,0)d(x2yz)=(x2yz)(1,1,1)(0,0,0)
=1 - 0 = 1

Alternately:
Equation of St. line x010=y010=z010=t(let)
x = y = z = t so dx = dy = dz = dt and 0t1
so, cV.dr=c(2xyzdx+x2zdy+x2ydz)

=104t3dt=1

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