If a constant force of (2 hat{i} + 3 hat{j} + | vedclass

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

Vedclass · Accepted Answer

$32$

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(A) The work done $W$ by a constant force $\vec{F}$ is given by the dot product of the force vector and the displacement vector $\vec{d}$.Given force $\vec{F} = (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) 	ext{ N}$.The initial position vector is $\vec{r}_1 = (3 \hat{i} - 4 \hat{k}) 	ext{ m}$.The final position vector is $\vec{r}_2 = (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) 	ext{ m}$.The displacement vector $\vec{d} = \vec{r}_2 - \vec{r}_1 = (2 - 3) \hat{i} + (2 - 0) \hat{j} + (3 - (-4)) \hat{k} = (-1 \hat{i} + 2 \hat{j} + 7 \hat{k}) 	ext{ m}$.Work done $W = \vec{F} \cdot \vec{d} = (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) \cdot (-1 \hat{i} + 2 \hat{j} + 7 \hat{k})$.$W = (2 	imes -1) + (3 	imes 2) + (4 	imes 7) = -2 + 6 + 28 = 32 	ext{ J}$.

If a constant force of $(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) \text{ N}$ acting on a body of mass $5 \text{ kg}$ displaces it from $(3 \hat{i} - 4 \hat{k}) \text{ m}$ to $(2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \text{ m}$, then the work done by the force on the body is (in $\text{ J}$)

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