A particle is acted upon by a force F→=(i^−2j^+k^)N . If the particle is at P(−1m, 2m, 3m) , the torque of the force about Q(2m, 3m, 1m) is

OP=−i^+2j^+3k^ OQ=2i^+3j^+k^OP−OQ=−3i^−j^+2k^OP−OQ=rr¯×F=|ijk−3−121−21|=i(−1+4)−j(−3−2)+k(6+1)=3i^+5j^+7k^ N−m

A particle is acted upon by a force F→=(i^−2j^+k^)N . If the particle is at P(−1m, 2m, 3m) , the torque of the force about Q(2m, 3m, 1m) is

OP=−i^+2j^+3k^ OQ=2i^+3j^+k^OP−OQ=−3i^−j^+2k^OP−OQ=rr¯×F=|ijk−3−121−21|=i(−1+4)−j(−3−2)+k(6+1)=3i^+5j^+7k^ N−m

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A particle is acted upon by a force $\vec{F} = (\hat{i} - 2 \hat{j} + \hat{k}) N$ . If the particle is at $P (- 1 m, 2 m, 3m)$ , the torque of the force about $Q (2m, 3m, 1m)$ is

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(\hat{i} - 3 \hat{j} + \hat{k}) N - m

(3 \hat{i} + 5 \hat{j} + 7 \hat{k}) N - m

(2 \hat{i} + 3 \hat{j} - \hat{k}) N - m

answer is C.

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Detailed Solution

$O P = - \hat{i} + 2 \hat{j} + 3 \hat{k}$

$O Q = 2 \hat{i} + 3 \hat{j} + \hat{k}$

$O P - O Q = - 3 \hat{i} - \hat{j} + 2 \hat{k}$

$O P - O Q = r$

$\bar{r} \times F = | \begin{matrix} i & j & k \\ - 3 & - 1 & 2 \\ 1 & - 2 & 1 \end{matrix} |$

$= i (- 1 + 4) - j (- 3 - 2) + k (6 + 1)$

$= 3 \hat{i} + 5 \hat{j} + 7 \hat{k} N - m$

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A particle is acted upon by a force F→=(i^−2j^+k^)N . If the particle is at P(−1m, 2m, 3m) , the torque of the force about Q(2m, 3m, 1m) is

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A particle is acted upon by a force $\vec{F} = (\hat{i} - 2 \hat{j} + \hat{k}) N$ . If the particle is at $P (- 1 m, 2 m, 3m)$ , the torque of the force about $Q (2m, 3m, 1m)$ is