The torque of force F→=2i→−3j→+4k→ newton acting at the point r→=3i→+2j→+3k→ metre about the origin is

F→=2i→−3j→+4k→ r→=3i→+2j→+3k→ τ=r→×F→×=|ijk3232−34| =i(8+9)−j(12−6)+k(−9−4) =17i^−6j^−13k^

The torque of force F→=2i→−3j→+4k→ newton acting at the point r→=3i→+2j→+3k→ metre about the origin is

F→=2i→−3j→+4k→ r→=3i→+2j→+3k→ τ=r→×F→×=|ijk3232−34| =i(8+9)−j(12−6)+k(−9−4) =17i^−6j^−13k^

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The torque of force $\vec{F} = 2 \vec{i} - 3 \vec{j} + 4 \vec{k}$ newton acting at the point $\vec{r} = 3 \vec{i} + 2 \vec{j} + 3 \vec{k}$ metre about the origin is

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- 6 \vec{i} + 6 \vec{j} - 12 \vec{k}

17 \vec{i} - 6 \vec{j} - 13 \vec{k}

6 \vec{i} - 6 \vec{j} + 12 \vec{k}

- 17 \vec{i} + 6 \vec{j} + 13 \vec{k}

answer is B.

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Detailed Solution

\vec{F} = 2 \vec{i} - 3 \vec{j} + 4 \vec{k}

$\vec{r} = 3 \vec{i} + 2 \vec{j} + 3 \vec{k}$

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

$= i (8 + 9) - j (12 - 6) + k (- 9 - 4)$

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

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The torque of force F→=2i→−3j→+4k→ newton acting at the point r→=3i→+2j→+3k→ metre about the origin is

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The torque of force $\vec{F} = 2 \vec{i} - 3 \vec{j} + 4 \vec{k}$ newton acting at the point $\vec{r} = 3 \vec{i} + 2 \vec{j} + 3 \vec{k}$ metre about the origin is