Question

The vector moment about the point $\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k}$ of the resultant of forces $\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{5k}$ and $\overrightarrow{3j}-\overrightarrow{4k}$ acting at the point $-\overrightarrow{2i}+\overrightarrow{3j}-\overrightarrow{3k}$ is

• A. $\overrightarrow{5i}+\overrightarrow{j}-\overrightarrow{4k}$
• B. $\overrightarrow{5i}-\overrightarrow{j}-\overrightarrow{4k}$
• C. $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{4k}$
• D. None of these

Answer 1

The correct option is D None of these

The moment of a force is given by $\overline{r}\times \overline{F}$ where $\overline{r}$ is the vector joining point action of force $\overline{F}$ and the point about which it is calculated.

Here, $\overline{r}=-3\overline{i}+\overline{j}-6\overline{k}$

$\overline{F}=\overline{i}+\overline{j}+\overline{k}$

$\overrightarrow{r}\times \overrightarrow{F}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ -3& 1& -6\\ 1& 1& 1\end{array}\right|$

$=7\hat{i}-3\hat{j}-4\hat{k}$

Moment is $7\overline{i}-3\overline{j}-4\overline{k}$