• # question_answer 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 a for which angular momentum about origin is conserved is A)  1             B)  -1C)  2             D)  zero

Angular momentum will be conserved if net torque acting on the system becomes zero. Given force acting $\vec{F}=\alpha \hat{i}+3\hat{j}+6\hat{k}$       (i) and $\vec{r}=2\hat{i}-6\hat{j}-12\hat{k}=-2(-\hat{i}+3\hat{j}+6\hat{k})$      (ii) If torque becomes zero then $\vec{r}\times \vec{F}=0$ If $\alpha =-1$then, $\vec{r}\times \vec{F}=0$