Question:
The work done by the force $4\hat{i} - 3\hat{j} + 2\hat{k}$ in moving a particle along a straight line from the point $(3, 2, -1)$ to $(2, -1, 4)$ is
The work done by the force $4\hat{i} - 3\hat{j} + 2\hat{k}$ in moving a particle along a straight line from the point $(3, 2, -1)$ to $(2, -1, 4)$ is
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Work done = $\mathbf{F} \cdot \mathbf{d}$. Always compute the displacement vector first: $\mathbf{d} = \text{final position} - \text{initial position}$.
Updated On: Apr 8, 2026
- 0 unit
- 4 unit
- 15 unit
- 19 unit
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Work done by a constant force $\mathbf{F}$ over displacement $\mathbf{d}$ equals $W = \mathbf{F} \cdot \mathbf{d}$.
Step 2: Detailed Explanation:
Displacement $\mathbf{d} = (2-3)\hat{i} + (-1-2)\hat{j} + (4-(-1))\hat{k} = -\hat{i} - 3\hat{j} + 5\hat{k}$.
$W = (4)(-1) + (-3)(-3) + (2)(5) = -4 + 9 + 10 = 15$ units.
Step 3: Final Answer:
Work done $= 15$ units.
Work done by a constant force $\mathbf{F}$ over displacement $\mathbf{d}$ equals $W = \mathbf{F} \cdot \mathbf{d}$.
Step 2: Detailed Explanation:
Displacement $\mathbf{d} = (2-3)\hat{i} + (-1-2)\hat{j} + (4-(-1))\hat{k} = -\hat{i} - 3\hat{j} + 5\hat{k}$.
$W = (4)(-1) + (-3)(-3) + (2)(5) = -4 + 9 + 10 = 15$ units.
Step 3: Final Answer:
Work done $= 15$ units.
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