Question

The work done by the force \( \mathbf{F} = (4\hat{i} -3\hat{j} + 2\hat{k}) \) N in giving a 1 nC charge a displacement of \( (10\hat{i} + 2\hat{j} -7\hat{k}) \) m is:

• A. 100 nJ
• B. 60 nJ
• C. 64 nJ
• D. 20 nJ

Hint:

Work done is calculated as \( W = \mathbf{F} \cdot \mathbf{d} \).

Answer 1

The Correct Option is C

The work done by a force is given by the dot product:
\[ W = \mathbf{F} \cdot \mathbf{d} \] \[ W = (4\hat{i} -3\hat{j} + 2\hat{k}) \cdot (10\hat{i} + 2\hat{j} -7\hat{k}) \] \[ W = (4 \times 10) + (-3 \times 2) + (2 \times -7) \] \[ W = 40 - 6 - 14 = 20 \text{ nJ} \]