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A force F = (3î - 2ĵ + 4k̂) N acts at the point r = (2î + ĵ - k̂) m…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A force $\vec{F} = (3\hat{i} - 2\hat{j} + 4\hat{k})\ \text{N}$ acts at the point $\vec{r} = (2\hat{i} + \hat{j} - \hat{k})\ \text{m}$ . Find the torque about the origin and its size, and check that it is at right angles to both $\vec{r}$ and $\vec{F}$ .

Need a reminder? The key ideaShow

The vector product $\vec{A} \times \vec{B}$ has size $AB\sin\theta$ and points at right angles to both (right-hand rule). From parts: $\vec{A} \times \vec{B} = (A_yB_z - A_zB_y)\hat{i} + (A_zB_x - A_xB_z)\hat{j} + (A_xB_y - A_yB_x)\hat{k}$ .

Torque about a point: $\vec{\tau} = \vec{r} \times \vec{F}$ , of size $rF\sin\theta$ , which is the force times its moment arm (the perpendicular distance from the point to the force's line).

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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