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Physics · WORK, ENERGY AND POWER
हिन्दीA force \( \mathbf{F} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}} - 5\hat{\mathbf{k}})\text{ N} \) acts on a particle and produces a displacement \( \mathbf{d} = (5\hat{\mathbf{i}} + 4\hat{\mathbf{j}} + 3\hat{\mathbf{k}})\text{ m} \). The cosine of the angle \( \theta \) between the force and displacement vectors is:
Correct answer · Option 2
\( 0.32 \)
Explanation
\( \mathbf{F}\cdot\mathbf{d} = (3)(5) + (4)(4) + (-5)(3) = 16\text{ J} \). The magnitudes are \( F = \sqrt{9+16+25} = \sqrt{50} \) and \( d = \sqrt{25+16+9} = \sqrt{50} \). Hence, \( \cos\theta = \frac{\mathbf{F}\cdot\mathbf{d}}{Fd} = \frac{16}{50} = 0.32 \).
