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}=\overset{\to }{\mathop{OP}}\,=-3,-3,4 $ $ \therefore $ Moment of F about $ O $ is $ \overrightarrow{r}\times \overrightarrow{F}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ -3 & -3 & 4 \\ -2 & 6 & -8 \\ \end{matrix} \right| $ $ =\hat{i}(0)-\hat{j}(32)+\hat{k}(-24) $ $ \therefore $ Magnitude $ =\sqrt{{{32}^{2}}+{{24}^{2}}} $ $ =40 $