Question

Find the moment of the forces $\overline{p_1}=2\hat{i}+\hat{j}+\hat{k}$ and $\overline{p_2}=2\hat{i}+2\hat{j}+2\hat{k}$ about the point $\overline{r}=(\hat{i}+\hat{j}+\hat{k})$

• A. $\hat{i}-\hat{j}+\hat{k}$
• B. $\hat{j}+\hat{k}$
• C. $-(\hat{j}-\hat{k})$
• D. $\hat{i}+\hat{j}-\hat{k}$

Answer 1

The correct option is C $-(\hat{j}-\hat{k})$

Net force $\overrightarrow{p}=\overrightarrow{p_1}+\overline{p_2}$
$=4\hat{i}+3\hat{j}+3\hat{k}$

$\therefore$ Moment for the force $=\overline{p}\times \overline{r}$

$=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 4& 3& 3\\ 1& 1& 1\end{array}\right|$

$=\hat{i}\left(0\right)-\hat{j}\left(l\right)+\hat{k}\left(l\right)$

$=-(\hat{j}-\hat{k})$