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 = \begin{vmatrix}\hat i & \hat j & \hat k \\7 & 3 & 1 \\-3 & 1 & 5 \\\end{vmatrix}$
$ = \hat i (15 - 1) - \hat j (35 + 3) + \hat k (7 + 9)$
$ = 14 \hat i - 38 \hat j + 16 \hat k$