Question

The magnitude of the moment of a force $-2\hat{i}+6\hat{j}-8\hat{k}$ acting at the point $-2\hat{i}-\hat{j}+3\hat{k}$ about the point $\hat{i}+2\hat{j}-\hat{k}$ is:

• A. $\sqrt{211}$
• B. $40$
• C. $\sqrt{54}$
• D. $2\sqrt{54}$
• E. $72$

Answer 1

Answer: (B)

Force $=-2\hat{i}+6\hat{j}-8\hat{k}$ Let $P(-2,-1,3)$ and $\text{O}(1,2,-1)$ Then $\overrightarrow{r}=\overrightarrow{\mathrm{OP}}=-3,-3,4$ $\therefore$ Moment of F about $O$ is $\overrightarrow{r}\times \overrightarrow{F}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ -3& -3& 4\\ -2& 6& -8\end{array}\right|$ $=\hat{i}(0)-\hat{j}(32)+\hat{k}(-24)$ $\therefore$ Magnitude $=\sqrt{{32}^2+{24}^2}$ $=40$