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  4. A uniform force of (3 hati + hatj) newton acts on a particle of mass 2kg. Hence the particle is displaced from position (2 hati + hatk ) meter to position (4 hati + 3 hatj - hatk) meter. The work done by the force on the particle is :

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Q. A uniform force of $(3 \hat{i} + \hat{j})$ newton acts on a particle of mass 2kg. Hence the particle is displaced from position$ (2\hat{i} + \hat{k} )$ meter to position $(4\hat{i} + 3\hat{j} - \hat{k})$ meter. The work done by the force on the particle is :

NEETNEET 2013Work, Energy and Power

Solution:

$W = \vec{F}. \vec{S} = (3\hat{i} + \hat{j}) .[(4 -2) \hat{i} + (3 - 0) \hat{j} + ( - 1 - 1)\hat{k}]$
$= (3\hat{i} + \hat{j}) .(2\hat{i} + 3 \hat{j} - 2\hat{k})$
$= 3(2) + 1(3) + 0( - 2) = 9 \,\,J $