Question

The moment force $\hat{i}+\hat{j}+\hat{k}$ acting through the point $A=-2\hat{i}+3\hat{j}+\hat{k}$ about the point $B=\hat{i}+2\hat{j}+3\hat{k}$ is

• A. $3\hat{i}+\hat{j}+4\hat{k}$
• B. $3\hat{i}-\hat{j}-4\hat{k}$
• C. $3\hat{i}+\hat{j}-4\hat{k}$
• D. $3\hat{i}-\hat{j}+4\hat{k}$

Answer 1

Answer: (C)

$3\hat{i}+\hat{j}-4\hat{k}$

$\overrightarrow{r}=\overrightarrow{B}-\overrightarrow{A}$
$=3\hat{i}-\hat{j}+2\hat{k}$
$\overrightarrow{F}=\hat{i}+\hat{k}+\hat{j}$
moment of force $M=\overrightarrow{r}\times \overrightarrow{f}$
$=(3\hat{i}-\hat{j}+2\hat{k})\times (\hat{i}+\hat{k}+\hat{j})$
$m=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -1& 2\\ 1& 1& 1\end{array}\right|=-3\hat{i}-\hat{j}+4\hat{k}$
$m=-3\hat{i}-\hat{j}+4\hat{k}$
or
$m=3\hat{i}+\hat{j}-4\hat{k}$