Question

The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at $(2, 0, - 3)$, about the point $(2, - 2, - 2)$, is given by

• A. $- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$
• B. $- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$
• C. $- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$
• D. $-4 \hat{i} - \hat{j} - 8 \hat{k}$

Answer 1

Answer: (A)

$\vec{\tau} = (\vec{r} - \vec{r}_0) \times \vec{F}$ .....(i)
$\vec{r} - \vec{r}_0 = (2 \hat{i} + 0 \hat{j} - 3 \hat{k}) - ( 2 \hat{i} - 2 \hat{j} - 2 \hat{k})$
$ = 0 \hat{i} + 2 \hat{j} - \hat{k}$
$\vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 0&2&-1\\ 4&5&-6\end{vmatrix} = - 7 \hat{i} - 4 \hat{j} - 8 \hat{k} $