Question

The moment of the force, $\overrightarrow{F}=4\hat{i}+5\hat{j}-6\hat{k}$ at $\left(2,0,–3\right)$ about the point $\left(2,–2,–2\right)$ 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 $-7\hat{i}-4\hat{j}-8\hat{k}$

$\overrightarrow{F}=4\hat{i}+5\hat{j}-6\hat{k}\overrightarrow{r}=\left(2-2\right)\hat{i}+\left(0+2\right)\hat{j}+\left(-3+2\right)\hat{k}=2\hat{j}-1\hat{k}\overrightarrow{r}\times \overrightarrow{F}=\left(2\hat{j}-1\hat{k}\right)\times \left(4\hat{i}+5\hat{j}-6\hat{k}\right)=\left(\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 0& 2& -1\\ 4& 5& -6\end{array}\right|=-7\hat{i}-4\hat{j}-8\hat{k}$