GATE 2024 AE – Question 30

Engineering Mathematics · Linear Algebra: Vector algebra, matrix algebra, systems of linear equations, rank, eigenvalues and eigenvectors · 1 mark · Numerical answer

A particle acted upon by a constant force $4\hat i + \hat j - 3\hat k$ N is displaced from point A with position vector $\hat i + 2\hat j + 3\hat k$ m to point B with position vector $5\hat i + 4\hat j + \hat k$ m. The work done by this force is _______ J (answer in integer).

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Correct answer: 24

Explanation

The displacement is $\vec d = (5 - 1)\hat i + (4 - 2)\hat j + (1 - 3)\hat k = 4\hat i + 2\hat j - 2\hat k$. The work is $\vec F\cdot\vec d = 16 + 2 + 6 = 24$ J.