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  4. A force (4 hati+ hatj-2 hatk)N acting on a body maintains its velocity at (2 hati+2 hatj+3 hatk)ms-1 . The power exerted is

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Q. A force $ (4\hat{i}+\hat{j}-2\hat{k})N $ acting on a body maintains its velocity at $ (2\hat{i}+2\hat{j}+3\hat{k})m{{s}^{-1}} $ . The power exerted is

KEAMKEAM 2010Work, Energy and Power

Solution:

Force, $ \vec{F} = \left(4\,\hat{i} + \hat{j}-2\hat{k}\right)\,N $
Velocity, $ \vec{v} = \left(2\,\hat{i} + 2\hat{j}+3\hat{k}\right)\,ms^{-1} $
Power, $ p = \vec{F} \cdot \vec{v} = \left(4\,\hat{i} + \hat{j}-2\hat{k}\right)\cdot\left(2\,\hat{i} + 2\hat{j}+3\hat{k}\right) $
$ = \left(8 + 2 - 6 \right)W = 4\,W $