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Question: The moment of the couple formed by the forces \(5\mathbf{i} + \mathbf{k}\) and \(- 5\mathbf{i} - \ma...

The moment of the couple formed by the forces 5i+k5\mathbf{i} + \mathbf{k} and −5i−k- 5\mathbf{i} - \mathbf{k} acting at the points (9,−1,2)(9, - 1,2) and (3,−2,1)(3, - 2,1) respectively is

A

−i+j+5k- \mathbf{i} + \mathbf{j} + 5\mathbf{k}

B

i−j−5k\mathbf{i} - \mathbf{j} - 5\mathbf{k}

C

2i−2j−10k2\mathbf{i} - 2\mathbf{j} - 10\mathbf{k}

D

−2i+2j+10k- 2\mathbf{i} + 2\mathbf{j} + 10\mathbf{k}

Answer

i−j−5k\mathbf{i} - \mathbf{j} - 5\mathbf{k}

Explanation

Solution

Moment of the couple,

=BA→×F→= \overset{\rightarrow}{BA} \times \overset{\rightarrow}{F}={(9−3)i+(−1+2)j+(2−1)k}×(5i+k)\{(9 - 3)\mathbf{i} + ( - 1 + 2)\mathbf{j} + (2 - 1)\mathbf{k}\} \times (5\mathbf{i} + \mathbf{k}) = (6i+j+k)×(5i+k)(6\mathbf{i} + \mathbf{j} + \mathbf{k}) \times (5\mathbf{i} + \mathbf{k}) = ∣ijk611501∣=i−j−5k\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 6 & 1 & 1 \\ 5 & 0 & 1 \end{matrix} \right| = \mathbf{i} - \mathbf{j} - 5\mathbf{k}