Physics - Vectors Question with Solution | TestHub

The torque $\vec{\tau }$ acting about the origin is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$.

$\vec{\tau }=\vec{r}\times \vec{F}$

Substituting the given vectors:

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

Using the determinant method for cross product:

$\vec{\tau }=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 7& 3& 1\\ -3& 1& 5\end{array}\right|$

$\vec{\tau }=\hat{i}(3\times 5-1\times 1)-\hat{j}(7\times 5-1\times (-3))+\hat{k}(7\times 1-3\times (-3))$

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

$\vec{\tau }=14\hat{i}-38\hat{j}+16\hat{k}$

Answer: $(14\hat{\mathrm{i}}-38\hat{\mathrm{j}}+16\hat{\mathrm{k}})$