Question

The torque about the point $3\hat{i}-\hat{j}+3\hat{k}$ of a force $4\hat{i}+2\hat{j}+\hat{k}$ through the point $5\hat{i}+2\hat{j}+4\hat{k}$, is

• A. $\hat{i}+2\hat{j}-8\hat{k}$
• B. $\hat{i}+2\hat{j}+8\hat{k}$
• C. $\hat{i}-2\hat{j}-8\hat{k}$
• D. $-\hat{i}-2\hat{j}-8\hat{k}$

Answer 1

Answer: (A)

$\hat{i}+2\hat{j}-8\hat{k}$

$\overrightarrow{r}=(3i-\hat{j}+3\hat{k})-(5\hat{i}+2\hat{j}+4\hat{k})$
$=-2\hat{i}-3\hat{j}-\hat{k}$
$T=\overrightarrow{r}\times \overrightarrow{F}$ (taught in physics)
$=(-2\hat{i}-3\hat{j}-\hat{k})\times (4\hat{i}+2\hat{j}+\hat{k})$
$T=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ -2& -3& -1\\ 4& 2& 1\end{array}\right|=-\hat{i}-2\hat{j}+8\hat{k}$
$T=-\hat{i}-2\hat{j}-8\hat{k}$
or
$\hat{i}+2\hat{j}-8\hat{k}$