A force \(\vec{F} = \alpha\hat{i} + 3\hat{j} + 6\hat{k}\) is acting at a point \(\vec{r} = 2\hat{i} - 6\hat{j} - 12\hat{k}\). The value of \(\alpha\) for which angular momentum about origin is conserved is :

- 1

Conservation of Angular Momentum ⇒ \(\tau = 0 \)

\(\vec{r} × \vec{F} = 0\)

 ⇒ \(\frac{F_x}{x} = \frac{F_y}{y} = \frac{F_z}{z} \)

\(\frac{\alpha}{2} = \frac{3}{-6} = \frac{6}{-12} \)

 ⇒ \(\alpha = -1 \)