A force $\overrightarrow{\mathrm{F}}=\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right) \mathrm{N}$ acts at a point ${\overrightarrow{\mathrm{r}}}_1=(2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+7\hat{\mathrm{k}}) \mathrm{m}.$ The torque of the force about the point ${\overrightarrow{\mathrm{r}}}_2=(\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}) \mathrm{m}$ is

A particle of mass $m$ is moving with constant velocity $v$ parallel to the $x$-axis as shown in the figure. Its angular momentum about origin $O$ is

A particle $P$ is moving along a straight line as shown in the figure. During the motion of the particle from $A$ to $B$ the angular momentum of the particle about $O$

For equilibrium of the system, value of mass $m$ should be