Question 44
Forces <span class="math-tex">\(4\hat{i}-3\hat{j}+7\hat{k}\)</span> and <span class="math-tex">\(-2\hat{i}+2\hat{j}-8\hat{k}\)</span> are acting on a particle and displaced it from the point (5, 7, 1) to (2, 5, -6), then the work done by the force is
๐ Step-by-Step Solution & Detailed Explanation:
Total force \(\vec{F} = (4 - 2)\hat{i} + (-3 + 2)\hat{j} + (7 - 8)\hat{k} = 2\hat{i} - \hat{j} - \hat{k}\)
Displacement \(\vec{d} = (2-5)\hat{i} + (5-7)\hat{j} + (-6-1)\hat{k} = -3\hat{i} - 2\hat{j} - 7\hat{k}\)
Work = \(\vec{F} \cdot \vec{d} = -6 + 2 + 7 = 3\)
Answer: (C) 3
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