Question

The force $7\hat i + 3 \hat j- 5\hat k$ acts on a particle whose position vector is $\hat i - \hat j +\hat k$ . What is the torque of a given force about the origin?

• A. $2\hat{i} +12\hat{j} +10\hat{k}$
• B. $2\hat{i} +10\hat{j} +12\hat{k}$
• C. $2\hat{i} +10\hat{j} +10\hat{k}$
• D. $10\hat{i} +2\hat{j} +\hat{k}$

Answer 1

Answer: (A)

Here, $\vec{r} = \hat{i} -\hat{j} +\hat{k} , \vec{F} = 7\hat{i} +3\hat{j} -5\hat{k}$
Torque, $\vec{\tau} = \vec{r} \times\vec{F} $
$\vec{\tau} = \begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\ 1&-1&1\\ 7&3&-5\end{vmatrix}$
$ = \hat{i} \left(5-3\right) + \hat{j} \left(7-\left(-5\right)\right) + \hat{k} \left(3-\left(-7\right)\right) $
or $\vec{\tau} = 2\hat{i} +12\hat{j} +10\hat{k}$