The moment of the force, F=4 i+5 j-6 k at (2, 0, -3), about the point (2, -2, -2), is given by

1. $-8\hat i-4\hat j-7\hat k$

2. $-7\hat i-8\hat j-4\hat k$

3. $-4\hat i-\hat j-8\hat k$

4. $-7\hat i-4\hat j-8\hat k$

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Answer: 4. $-7\hat i-4\hat j-8\hat k$

Moment (torque) about a point: $\vec\tau=\vec r\times\vec F$, where $\vec r$ goes from the point to the point of application.

$\vec r=(2,0,-3)-(2,-2,-2)=(0,2,-1)$, $\vec F=(4,5,-6)$.

$$\vec\tau=\begin{vmatrix}\hat i&\hat j&\hat k\\0&2&-1\\4&5&-6\end{vmatrix}=\hat i(-12+5)-\hat j(0+4)+\hat k(0-8)=-7\hat i-4\hat j-8\hat k$$

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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