Question

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

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

Answer 1

Answer: (A)

$\vec{\tau }=(\vec{r}-{\vec{r}}_0)\times \vec{F}$ .....(i)
$\vec{r}-{\vec{r}}_0=(2\hat{i}+0\hat{j}-3\hat{k})-(2\hat{i}-2\hat{j}-2\hat{k})$
$=0\hat{i}+2\hat{j}-\hat{k}$
$\vec{\tau }=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 0& 2& -1\\ 4& 5& -6\end{array}\right|=-7\hat{i}-4\hat{j}-8\hat{k}$