A particle of mass $1 kg$ located at the position  $(i+j )m$has a velocity  $2\left( \hat{i}- \hat{j}+ \hat{k}\right)\raisebox{1ex}{$ m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. Its angular momentum about $z$-axis is 

Velocity of the particle perpendicular to $z-$axis is $\overrightarrow{v}=2\left( \hat{i}- \hat{j}\right)$ . Angular momentum about $z$-axis

$$\begin{gathered} \overrightarrow{ L}=m(\overrightarrow{r}\times \overrightarrow{v}) \\ =1\left[\left( \hat{i}+ \hat{j}\right)\times \left( 2\hat{i}-2 \hat{j}\right)\right] \\ \overrightarrow{ L}=-2 \hat{k}-2 \hat{k}=-4 kg-m^2/s \end{gathered}$$