A force vec{F} = (-2hat{i} + 15hat{j} + 6hat{ | vedclass

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(B) The work done $W$ by a constant force is given by the dot product of the force vector $\vec{F}$ and the displacement vector $\vec{S}$.Given: $\vec

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$150$

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(B) The work done $W$ by a constant force is given by the dot product of the force vector $\vec{F}$ and the displacement vector $\vec{S}$.Given: $\vec{F} = (-2\hat{i} + 15\hat{j} + 6\hat{k}) \, N$.The displacement is along the $Y$-axis by $10 \, m$,so $\vec{S} = 10\hat{j} \, m$.Work $W = \vec{F} \cdot \vec{S} = (-2\hat{i} + 15\hat{j} + 6\hat{k}) \cdot (10\hat{j})$.Using the dot product property $\hat{i} \cdot \hat{j} = 0$,$\hat{j} \cdot \hat{j} = 1$,and $\hat{k} \cdot \hat{j} = 0$:$W = (-2 	imes 0) + (15 	imes 10) + (6 	imes 0) = 150 \, J$.

$A$ force $\vec{F} = (-2\hat{i} + 15\hat{j} + 6\hat{k}) \, N$ acts on an object,causing it to move along the $Y$-axis. If the displacement along the $Y$-axis is $10 \, m$,find the work done by the force in $J$.

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