If a force (3 hat{i} + 2 hat{j} + 5 hat{k}) t | vedclass

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Question

(C) The work done $W$ by a constant force $\vec{F}$ during a displacement $\vec{d}$ is given by the dot product of the force and displacement vectors:

Vedclass · Accepted Answer

$15$

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(C) The work done $W$ by a constant force $\vec{F}$ during a displacement $\vec{d}$ is given by the dot product of the force and displacement vectors:$W = \vec{F} \cdot \vec{d}$Given:$\vec{F} = (3 \hat{i} + 2 \hat{j} + 5 \hat{k}) 	ext{ N}$$\vec{d} = (2 \hat{i} + 2 \hat{j} + 1 \hat{k}) 	ext{ m}$Calculating the dot product:$W = (3 \hat{i} + 2 \hat{j} + 5 \hat{k}) \cdot (2 \hat{i} + 2 \hat{j} + 1 \hat{k})$$W = (3 	imes 2) + (2 	imes 2) + (5 	imes 1)$$W = 6 + 4 + 5$$W = 15 	ext{ J}$Therefore,the work done is $15 	ext{ J}$.

If a force $(3 \hat{i} + 2 \hat{j} + 5 \hat{k}) \text{ N}$ acting on a body displaces it through $(2 \hat{i} + 2 \hat{j} + 1 \hat{k}) \text{ m}$,then the work done by the force on the body is (in $J$)

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