Find the torque about the origin when a force of 3j^ N3\hat{j} \text{ N}3j^ N acts on a particle whose position vector is 2k^ m2\hat{k} \text{ m}2k^ m.
6i^ Nm6\hat{i} \text{ Nm}6i^ Nm
6j^ Nm6\hat{j} \text{ Nm}6j^ Nm
−6i^ Nm-6\hat{i} \text{ Nm}−6i^ Nm
6k^ Nm6\hat{k} \text{ Nm}6k^ Nm
The torque τ⃗=r⃗×F⃗\vec{\tau} = \vec{r} \times \vec{F}τ=r×F. Given r⃗=2k^ m\vec{r} = 2\hat{k} \text{ m}r=2k^ m and F⃗=3j^ N\vec{F} = 3\hat{j} \text{ N}F=3j^ N. Thus, τ⃗=2k^×3j^=6(k^×j^)=6(−i^)=−6i^ Nm\vec{\tau} = 2\hat{k} \times 3\hat{j} = 6(\hat{k} \times \hat{j}) = 6(-\hat{i}) = -6\hat{i} \text{ Nm}τ=2k^×3j^=6(k^×j^)=6(−i^)=−6i^ Nm.
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