A small particle moves to position 5 hat{i}-2 | vedclass

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Question

(B) The work done $W$ by a constant force $\vec{F}$ is given by the dot product of the force and the displacement vector $\vec{d} = \vec{r}_f - \vec{r

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(B) The work done $W$ by a constant force $\vec{F}$ is given by the dot product of the force and the displacement vector $\vec{d} = \vec{r}_f - \vec{r}_i$.Given:Force $\vec{F} = 5 \hat{i} + 2 \hat{j} + 7 \hat{k} 	ext{ N}$Initial position $\vec{r}_i = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$Final position $\vec{r}_f = 5 \hat{i} - 2 \hat{j} + \hat{k}$Displacement $\vec{d} = \vec{r}_f - \vec{r}_i = (5-2) \hat{i} + (-2-3) \hat{j} + (1 - (-4)) \hat{k} = 3 \hat{i} - 5 \hat{j} + 5 \hat{k}$Work done $W = \vec{F} \cdot \vec{d} = (5 \hat{i} + 2 \hat{j} + 7 \hat{k}) \cdot (3 \hat{i} - 5 \hat{j} + 5 \hat{k})$$W = (5 	imes 3) + (2 	imes -5) + (7 	imes 5)$$W = 15 - 10 + 35 = 40 	ext{ J}$.

$A$ small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k}$ from its initial position $2 \hat{i}+3 \hat{j}-4 \hat{k}$ under the action of force $5 \hat{i}+2 \hat{j}+7 \hat{k} \text{ N}$. The value of work done will be $............ \text{ J}$.

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