Question

Find the torque of a force $\overrightarrow{F}=-3\hat{i}+\hat{j}+5\hat{k}$ acting at the point $\overrightarrow{r}=7\hat{i}+3\hat{j}+\hat{k}$

• A. $14\hat{i}-38\hat{j}+16\hat{k}$
• B. $4\hat{i}-4\hat{j}+6\hat{k}$
• C. $ -13-16\hat { k } -38\hat { j } -16\hat { i } $
• D. none of these

Answer 1

The correct option is C $ -13-16\hat { k } -38\hat { j } -16\hat { i } $

$\overline{C}=\overline{F}.\overline{r}$

$=(-3\hat{i}+\hat{j}+5\hat{k})\times (7\hat{i}+3\hat{j}+\hat{k})$

$=(-3\hat{i}+\hat{j}+5\hat{k})\times (7\hat{i}+3\hat{j}+\hat{k})$

$=-3\hat{i}(7\hat{i}+3\hat{j}+\hat{k})+\hat{j}(7\hat{i}+3\hat{j}+\hat{k})+5\hat{k}(7\hat{i}+3\hat{j}+\hat{k})$

$=-21-9\hat{k}-3\hat{j}+(-7\hat{k})+3+(-1\hat{i})+(-35\hat{j})-15\hat{i}+5$

$=-21+8-16\hat{k}-3\hat{j}-\hat{i}-35\hat{j}-15\hat{i}$

$=-13-16\hat{k}-38\hat{j}-16\hat{i}$