Question

Find the torque about origin when a force of $6\hat{i}+3\hat{j}$ acts on a particle whose position vector is $3\hat{j}+5\hat{k}$

• A. $21\hat{k}$
• B. $15\hat{i}-30\hat{j}+18\hat{k}$
  
• C. $-15\hat{i}+30\hat{j}-18\hat{k}$
• D. $15\hat{i}+18\hat{k}$

Answer 1

The correct option is C $-15\hat{i}+30\hat{j}-18\hat{k}$

Torque of a force is given by
$\tau =\overrightarrow{r}\times \overrightarrow{F}\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 0& 3& 5\\ 6& 3& 0\end{array}\right|$
$\tau =\hat{i}[0-15]-\hat{j}[0-30]+\hat{k}[0-18]$
$\tau =-15\hat{i}+30\hat{j}-18\hat{k}$