A force (5i^+7j^−3k^)N acts on a particle at position (i^+j^−k^)m. Find torque of this force on the particle about origin

τ→=r→×F→=i^j^k^11−157−3=i^(−3+7)−j^(−3+5)+k^(7−5)=(4i^−2j^+2k^)N−m

A force (5i^+7j^−3k^)N acts on a particle at position (i^+j^−k^)m. Find torque of this force on the particle about origin

τ→=r→×F→=i^j^k^11−157−3=i^(−3+7)−j^(−3+5)+k^(7−5)=(4i^−2j^+2k^)N−m

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A force $(5 \hat{i} + 7 \hat{j} - 3 \hat{k}) N$ acts on a particle at position $(\hat{i} + \hat{j} - \hat{k}) m$ . Find torque of this force on the particle about origin

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$(4 \hat{i} + 2 \hat{j} + 2 \hat{k}) N - m$

$(4 \hat{i} - 2 \hat{j} + 2 \hat{k}) N - m$

$(- 4 \hat{i} + 2 \hat{j} - 2 \hat{k}) N - m$

$(10 \hat{i} - 8 \hat{j} + 12 \hat{k}) N - m$

answer is B.

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Detailed Solution

$\begin{array}{l} \vec{τ} = \vec{r} \times \vec{F} = |\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & - 1 \\ 5 & 7 & - 3 \end{array}| \\ = \hat{i} (- 3 + 7) - \hat{j} (- 3 + 5) + \hat{k} (7 - 5) = (4 \hat{i} - 2 \hat{j} + 2 \hat{k}) N - m \end{array}$