A force vec{F} = (5 hat{imath} - 2 hat{jmath} | vedclass

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(C) The work done $W$ by a constant force $\vec{F}$ is given by the dot product of force and displacement: $W = \vec{F} \cdot \vec{d}$.First,calculate

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) The work done $W$ by a constant force $\vec{F}$ is given by the dot product of force and displacement: $W = \vec{F} \cdot \vec{d}$.First,calculate the displacement vector $\vec{d} = \vec{r_2} - \vec{r_1}$.$\vec{d} = (6 - 3) \hat{\imath} + (-1 - 2) \hat{\jmath} + (4 - (-1)) \hat{k} = 3 \hat{\imath} - 3 \hat{\jmath} + 5 \hat{k} 	ext{ m}$.Now,calculate the work done:$W = (5 \hat{\imath} - 2 \hat{\jmath} + 3 \hat{k}) \cdot (3 \hat{\imath} - 3 \hat{\jmath} + 5 \hat{k})$.$W = (5 	imes 3) + (-2 	imes -3) + (3 	imes 5) = 15 + 6 + 15 = 36 	ext{ J}$.

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