Question

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

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

Answer 1

The correct option is D $-7\hat{i}-4\hat{j}-8\hat{k}$

The force given as $\overline{F}=4\overrightarrow{j}+5\overrightarrow{j}-6\overrightarrow{k}$

The force acting the point $(2,0,-3)$

The point under construction $(2,-2,-2)$

Position vector $(2,0,-3)$ w.r.to $(2,-2,-2)$

$\overrightarrow{r}=(2-2)i+(0-(-2\left)\right)j+(-3-2)\overrightarrow{k}=0\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k}$

moment of force is $\overrightarrow{M}=\overrightarrow{r}\times \overrightarrow{f}$

$M=(0i+2\overrightarrow{j}-\overrightarrow{k})\times (4i+4j-6\overrightarrow{k})$

$M=\left|\begin{array}{ccc}i& j& k\\ 0& 2& -1\\ 4& 5& -6\end{array}\right|=-7\overrightarrow{i}-4\overrightarrow{j}-8\overrightarrow{k}$