The torque of the force F→ = (2i^−3j^+4k^) N acting at the point r→ = (3i^+2j^+3k^) m about the origin be:

τ→ = r→ ×F→ = i^j^k^3232−34= [2×4−(3×−3)]i^+[2×3−3×4]j^+[3×−3−2×2]k^ = 17i^−6j^ −13k^

The torque of the force F→ = (2i^−3j^+4k^) N acting at the point r→ = (3i^+2j^+3k^) m about the origin be:

τ→ = r→ ×F→ = i^j^k^3232−34= [2×4−(3×−3)]i^+[2×3−3×4]j^+[3×−3−2×2]k^ = 17i^−6j^ −13k^

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The torque of the force $\vec{F} = (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) N acting at the point \vec{r} = (3 \hat{i} + 2 \hat{j} + 3 \hat{k}) m about the origin be$ :

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$6 \hat{i} - 6 \hat{j} + 12 \hat{k}$

$17 \hat{i} - 6 \hat{j} - 13 \hat{k}$

$- 6 \hat{i} + 6 \hat{j} - 12 \hat{k}$

$- 17 \hat{i} + 6 \hat{j} + 13 \hat{k}$

answer is B.

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

$\begin{array}{l} = [(2 \times 4) - (3 \times - 3)] \hat{i} + [(2 \times 3) - (3 \times 4)] \hat{j} + [(3 \times - 3) - (2 \times 2)] \hat{k} \end{array}$

= $17 \hat{i} - 6 \hat{j} - 13 \hat{k}$

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The torque of the force F→ = (2i^−3j^+4k^) N acting at the point r→ = (3i^+2j^+3k^) m about the origin be:

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The torque of the force $\vec{F} = (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) N acting at the point \vec{r} = (3 \hat{i} + 2 \hat{j} + 3 \hat{k}) m about the origin be$ :