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Physics · WORK, ENERGY AND POWER
हिन्दीTwo forces \( \mathbf{F}_1 = 3\hat{\mathbf{i}} + 4\hat{\mathbf{j}} - 5\hat{\mathbf{k}} \) and \( \mathbf{F}_2 = \hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 3\hat{\mathbf{k}} \) act concurrently on a particle, producing a displacement \( \mathbf{d} = 5\hat{\mathbf{i}} + 4\hat{\mathbf{j}} + 3\hat{\mathbf{k}} \). The cosine of the angle between the net force and the displacement vector is:
Correct answer · Option 3
\( \frac{22}{\sqrt{24}\sqrt{50}} \)
Explanation
\( \mathbf{F}_{\text{net}} = 4\hat{\mathbf{i}} + 2\hat{\mathbf{j}} - 2\hat{\mathbf{k}} \). \( |\mathbf{F}_{\text{net}}| = \sqrt{16+4+4} = \sqrt{24} \). \( |\mathbf{d}| = \sqrt{25+16+9} = \sqrt{50} \). \( \mathbf{F}_{\text{net}} \cdot \mathbf{d} = 20 + 8 - 6 = 22 \). Thus \( \cos\theta = \frac{22}{\sqrt{24}\sqrt{50}} \).
