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

A
$6 \hat{i} - 6 \hat{j} + 12 \hat{k}$
B
$17 \hat{i} - 6 \hat{j} - 13 \hat{k}$
C
$- 6 \hat{i} + 6 \hat{j} - 12 \hat{k}$
D
$- 17 \hat{i} + 6 \hat{j} + 13 \hat{k}$

Solution:

$\vec{τ} = \vec{r} \times \vec{F} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 2 & 3 \\ 2 & - 3 & 4 \end{matrix}|$
$= \hat{i} [8 - (- 9)] - \hat{j} (12 - 6) + \hat{k} (- 9 - 4)$
$= 17 \hat{i} - 6 \hat{j} - 13 \hat{k}$

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

Solution:

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