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 $F$ and displacement $d$. Given, force $F = 2 \hat{i} - \hat{j} - \hat{k}$. Th

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$9 	ext{ units}$

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

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

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