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Physics · WORK, ENERGY AND POWER
हिन्दीA particle moves in the \( x-y-z \) coordinate system under a constant force \( \mathbf{F} = (-2\hat{i} + 3\hat{j} + 4\hat{k})\text{ N} \). If it is displaced from point \( A(1, 2, -1)\text{ m} \) to point \( B(3, -1, 3)\text{ m} \), the total work done by the force is:
Correct answer · Option 4
\( 3\text{ J} \)
Explanation
Displacement vector \( \mathbf{d} = (3-1)\hat{i} + (-1-2)\hat{j} + (3 - (-1))\hat{k} = 2\hat{i} - 3\hat{j} + 4\hat{k} \). Work done \( W = \mathbf{F}\cdot\mathbf{d} = (-2)(2) + (3)(-3) + (4)(4) = -4 - 9 + 16 = 3\text{ J} \).
