What is the torque of the force F→ = (2i^-3j^ + 4k^ ) N acting at the point r=3i^ + 2j^+3k^m about the origin?

What is the torque of the force  N acting at the point m about the origin?

1. A

2. B

$17\stackrel{^}{\mathrm{i}}-6\stackrel{^}{\mathrm{j}}-13\stackrel{^}{\mathrm{k}}$

3. C

4. D

$-17\stackrel{^}{\mathrm{i}}+6\stackrel{^}{\mathrm{j}}+13\stackrel{^}{\mathrm{k}}$

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Solution:

$\stackrel{\to }{\mathrm{\tau }}=\stackrel{\to }{\mathrm{r}}×\stackrel{\to }{\mathrm{F}}=\left|\begin{array}{ccc}\stackrel{^}{\mathrm{i}}& \stackrel{^}{\mathrm{j}}& \stackrel{^}{\mathrm{k}}\\ 3& 2& 3\\ 2& -3& 4\end{array}\right|$
$=\stackrel{^}{\mathrm{i}}\left[8-\left(-9\right)\right]-\stackrel{^}{\mathrm{j}}\left(12-6\right)+\stackrel{^}{\mathrm{k}}\left(-9-4\right)$
$=17\stackrel{^}{\mathrm{i}}-6\stackrel{^}{\mathrm{j}}-13\stackrel{^}{\mathrm{k}}$

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