Question

Find the torque of a force $F=-3\hat{i}+\hat{j}+5\hat{k}$ acting at the point $r=7\hat{i}+3\hat{j}+\hat{k}$

• A. $14\hat{i}-38\hat{j}+16\hat{k}$
• B. $4\hat{i}+4\hat{j}+6\hat{k}$
• C. $-14\hat{i}+38\hat{j}-16\hat{k}$
• D. $-21\hat{i}+3\hat{j}+5\hat{k}$

Answer 1

Answer: (A)

Torque is defined as the cross product of force vector $F$ and $r$,
distance from the axis of rotation to the point on which the force is acting.
$\therefore \tau =r\times F$
Given $\tau =7\hat{i}+3\hat{j}+\hat{k}$,
$F=-3\hat{i}+\hat{j}+5\hat{k}$
$\tau =\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 7& 3& 1\\ -3& 1& 5\end{array}\right|$
$=\hat{i}(15-1)-\hat{j}(35+3)+\hat{k}(7+9)$
$=14\hat{i}-38\hat{j}+16\hat{k}$