Question

The line of action of a force $\overrightarrow{F}=\left(\begin{array}{c}-3\hat{i}+\hat{j}+5\hat{k}\end{array}\right)N$ passes through a point $(7,3,1)$. The moment of force $(\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F})$ about the origin is given by

• A. $14\hat{i}+38\hat{j}+16\hat{k}$
• B. $14\hat{i}+38\hat{j}-16\hat{k}$
• C. $14\hat{i}-38\hat{j}+16\hat{k}$
• D. $14\hat{i}-38\hat{j}-16\hat{k}$

Answer 1

The correct option is C $14\hat{i}-38\hat{j}+16\hat{k}$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 7& 3& 1\\ -3& 1& 5\end{array}\right|=14\hat{i}-38\hat{j}+16\hat{k}$