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A force vecF = 2 x hati + 2 hatj + 3z^(2...

A force `vecF = 2 x hati + 2 hatj + 3z^(2)hatk N` is acting on a particle .Find the work done by this force in displacing the body from `(1, 2, 3) m` to `(3,6,1)m`

Text Solution

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Work done `underset(x_(1)) overset(x_(2))(int) F_(x) dx + underset(y_(1)) overset(y_(2)) (int) F_(y) dy + underset(z_(1)) overset(z_(2)) (int) F_(z) dz`
`W = underset(1) overset(3)(int) 2xdx + underset(2) overset(6)(int) 2dy + underset(3) overset(1)(int) 3z^(2) dz`
`W =2[(x^(2))/(2)]_(1)^(3) + 2[y]_(2)^(6) + 3[(z^(3))/(3)]_(3)^(1) = -10 J`.
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