A particle is acted upon by constant forces 4i+j-3k and 3i+j-k which displace it from a point i+2j+3k to the point 5i+4j+k. The work done in standard - Mathematics MCQ AIEEE 2004 2026 | ExamTest.live

hardMCQAIEEE 20042026Mathematics

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A particle is acted upon by constant forces 4 \hat{i} + \hat{j} - 3 \hat{k} and 3 \hat{i} + \hat{j} - \hat{k} which displace it from a point \hat{i} + 2 \hat{j} + 3 \hat{k} to the point 5 \hat{i} + 4 \hat{j} + \hat{k} . The work done in standard units by the forces is given by

Solution & Step-by-step Explanation

Total force F = F_{1} + F_{2} = (4 \hat{i} + \hat{j} - 3 \hat{k}) + (3 \hat{i} + \hat{j} - \hat{k}) = 7 \hat{i} + 2 \hat{j} - 4 \hat{k} . Displacement d = r_{f ina l} - r_{ini t ia l} = (5 \hat{i} + 4 \hat{j} + \hat{k}) - (\hat{i} + 2 \hat{j} + 3 \hat{k}) = 4 \hat{i} + 2 \hat{j} - 2 \hat{k} . Work done W = F \cdot d : W = (7 \hat{i} + 2 \hat{j} - 4 \hat{k}) \cdot (4 \hat{i} + 2 \hat{j} - 2 \hat{k}) W = (7 \times 4) + (2 \times 2) + (- 4 \times - 2) = 28 + 4 + 8 = 40 .

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A particle is acted upon by constant forces 4 \hat{i} + \hat{j} - 3 \hat{k} and 3 \hat{i} + \hat{j} - \hat{k} which displace it from a point \hat{i} + 2 \hat{j} + 3 \hat{k} to the point 5 \hat{i} + 4 \hat{j} + \hat{k} . The work done in standard units by the forces is given by

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