What is torque of the force $\vec{F} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ acting at the point $\vec{r} = 3\hat{i} + 2\hat{j} + 3\hat{k}$ about origin? (1995)

$-6\hat{i} + 6\hat{j} - 12\hat{k}$

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

$6\hat{i} - 6\hat{j} + 12\hat{k}$

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

Solution:

Torque is $\vec{\tau} = \vec{r} \times \vec{F}$.
$\vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 2 & 3 \\ 2 & -3 & 4 \end{vmatrix}$.
$= \hat{i}(8 - (-9)) - \hat{j}(12 - 6) + \hat{k}(-9 - 4) = 17\hat{i} - 6\hat{j} - 13\hat{k}$.

Rankers Physics

What is torque of the force $\vec{F} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ acting at the point $\vec{r} = 3\hat{i} + 2\hat{j} + 3\hat{k}$ about origin? (1995)

Solution: