If force F→=3i^+4j^−2k^ acts on a particle having position vector 2i^+j^+2k^ then, the torque about the origin will be:

τ→=r→×F→=i^j^k^21234−2=i^(−2−8)−j^(−4−6)+k^(8−3)=−10i^+10j^+5k^

If force F→=3i^+4j^−2k^ acts on a particle having position vector 2i^+j^+2k^ then, the torque about the origin will be:

τ→=r→×F→=i^j^k^21234−2=i^(−2−8)−j^(−4−6)+k^(8−3)=−10i^+10j^+5k^

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If force $\vec{F} = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ acts on a particle having position vector $2 \hat{i} + \hat{j} + 2 \hat{k}$ then, the torque about the origin will be:

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$3 \hat{i} + 4 \hat{j} - 2 \hat{k}$

$- 10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

$10 \hat{i} + 5 \hat{j} - 10 \hat{k}$

$10 \hat{i} + \hat{j} - 5 \hat{k}$

answer is B.

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$\begin{aligned} \vec{τ} = \vec{r} \times \vec{F} \\ = |\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & 2 \\ 3 & 4 & - 2 \end{array}| \end{aligned}$

$\begin{aligned} = \hat{i} (- 2 - 8) - \hat{j} (- 4 - 6) + \hat{k} (8 - 3) \\ = - 10 \hat{i} + 10 \hat{j} + 5 \hat{k} \end{aligned}$

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If force F→=3i^+4j^−2k^ acts on a particle having position vector 2i^+j^+2k^ then, the torque about the origin will be:

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If force $\vec{F} = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ acts on a particle having position vector $2 \hat{i} + \hat{j} + 2 \hat{k}$ then, the torque about the origin will be: