Question:
A uniform force of \((4i + 3j) N acts on a body. The body is displaced from (4i - 3j - 2k)\,m to (5i - 4j + 2k)\,m. Then the work done by the force on the body is in joule:
A uniform force of \((4i + 3j) N acts on a body. The body is displaced from (4i - 3j - 2k)\,m to (5i - 4j + 2k)\,m. Then the work done by the force on the body is in joule:
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Work done by a force depends only on the dot product of force and displacement vectors, not on the path taken.
Updated On: Jun 19, 2026
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The Correct Option is A
Solution and Explanation
Step 1: Identify given force vector.
The force acting on the body is: \[ \vec{F} = 4\mathbf{i} + 3\mathbf{j} \]
Step 2: Find displacement vector.
Initial position: \[ \vec{r_1} = 4\mathbf{i} - 3\mathbf{j} - 2\mathbf{k} \] Final position: \[ \vec{r_2} = 5\mathbf{i} - 4\mathbf{j} + 2\mathbf{k} \] So displacement: \[ \vec{d} = \vec{r_2} - \vec{r_1} \] \[ = (5-4)\mathbf{i} + (-4+3)\mathbf{j} + (2+2)\mathbf{k} \] \[ = \mathbf{i} - \mathbf{j} + 4\mathbf{k} \]
Step 3: Work done formula.
Work done by a constant force: \[ W = \vec{F} \cdot \vec{d} \]
Step 4: Compute dot product.
\[ W = (4\mathbf{i} + 3\mathbf{j}) \cdot (\mathbf{i} - \mathbf{j} + 4\mathbf{k}) \] \[ = 4(1) + 3(-1) + 0(4) \]
Step 5: Simplify expression.
\[ W = 4 - 3 = 1 \]
Step 6: Final conclusion.
Thus, the work done by the force is: \[ \boxed{1 \, J} \]
The force acting on the body is: \[ \vec{F} = 4\mathbf{i} + 3\mathbf{j} \]
Step 2: Find displacement vector.
Initial position: \[ \vec{r_1} = 4\mathbf{i} - 3\mathbf{j} - 2\mathbf{k} \] Final position: \[ \vec{r_2} = 5\mathbf{i} - 4\mathbf{j} + 2\mathbf{k} \] So displacement: \[ \vec{d} = \vec{r_2} - \vec{r_1} \] \[ = (5-4)\mathbf{i} + (-4+3)\mathbf{j} + (2+2)\mathbf{k} \] \[ = \mathbf{i} - \mathbf{j} + 4\mathbf{k} \]
Step 3: Work done formula.
Work done by a constant force: \[ W = \vec{F} \cdot \vec{d} \]
Step 4: Compute dot product.
\[ W = (4\mathbf{i} + 3\mathbf{j}) \cdot (\mathbf{i} - \mathbf{j} + 4\mathbf{k}) \] \[ = 4(1) + 3(-1) + 0(4) \]
Step 5: Simplify expression.
\[ W = 4 - 3 = 1 \]
Step 6: Final conclusion.
Thus, the work done by the force is: \[ \boxed{1 \, J} \]
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