The work done in moving an object from the or | vedclass

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(B) We know that the work done $W$ is given by the dot product of force $\vec{F}$ and displacement $\vec{d}$.Given,force $\vec{F} = 2 \hat{i} - \hat{j

Vedclass · Accepted Answer

$9 	ext{ units}$

Vedclass · Answer

(B) We know that the work done $W$ is given by the dot product of force $\vec{F}$ and displacement $\vec{d}$.Given,force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$.The object moves from the origin $(0, 0, 0)$ to the position vector $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$,so the displacement $\vec{d} = \vec{r} - 0 = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$.Using the property of dot product $\hat{i} \cdot \hat{i} = \hat{j} \cdot \hat{j} = \hat{k} \cdot \hat{k} = 1$ and $\hat{i} \cdot \hat{j} = \hat{j} \cdot \hat{k} = \hat{k} \cdot \hat{i} = 0$,we calculate:$W = \vec{F} \cdot \vec{d} = (2 \hat{i} - \hat{j} - \hat{k}) \cdot (3 \hat{i} + 2 \hat{j} - 5 \hat{k})$$W = (2 	imes 3) + (-1 	imes 2) + (-1 	imes -5)$$W = 6 - 2 + 5 = 9 	ext{ units}$.

The work done in moving an object from the origin to a point whose position vector is $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$ is:

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