A force overrightarrow{F} = 5hat{i} + 6hat{j} | vedclass

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(A) The work done $W$ by a constant force $\overrightarrow{F}$ is given by the dot product of the force vector and the displacement vector $\overright

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$10$

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(A) The work done $W$ by a constant force $\overrightarrow{F}$ is given by the dot product of the force vector and the displacement vector $\overrightarrow{S}$.$W = \overrightarrow{F} \cdot \overrightarrow{S}$Given $\overrightarrow{F} = 5\hat{i} + 6\hat{j} + 4\hat{k}$ and $\overrightarrow{S} = 6\hat{i} + 0\hat{j} - 5\hat{k}$.$W = (5\hat{i} + 6\hat{j} + 4\hat{k}) \cdot (6\hat{i} + 0\hat{j} - 5\hat{k})$Using the property $\hat{i} \cdot \hat{i} = 1$,$\hat{j} \cdot \hat{j} = 1$,$\hat{k} \cdot \hat{k} = 1$ and cross-terms are $0$:$W = (5 	imes 6) + (6 	imes 0) + (4 	imes -5)$$W = 30 + 0 - 20$$W = 10 \ J$.

$A$ force $\overrightarrow{F} = 5\hat{i} + 6\hat{j} + 4\hat{k}$ acting on a body produces a displacement $\overrightarrow{S} = 6\hat{i} - 5\hat{k}$. The work done by the force is: (in $J$)

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