The position vector of a particle is $\vec{r} = (\hat{i} + 2\hat{j} - \hat{k})$ and its momentum is $\vec{p} = (3\hat{i} + 4\hat{j} - 2\hat{k})$. The angular momentum of this particle is perpendicular to:

$A$ mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency $\omega$. The mass $M$ moves with steady speed in a circular path of constant radius $r$. The angular momentum of $M$ about point $A$ is $L_A$,which lies in the positive $z$-direction,and the angular momentum of $M$ about point $B$ is $L_B$. Which of the following statements is correct for this system?

The angular momentum of a system of particles changes if:

Find the components along the $x, y, z$ axes of the angular momentum $\vec{l}$ of a particle whose position vector is $\vec{r}$ with components $x, y, z$ and momentum is $\vec{p}$ with components $p_x, p_y, p_z$. Show that if the particle moves only in the $x-y$ plane,the angular momentum has only a $z$-component.

Two particles $A$ and $B$ are moving as shown in the figure. Their total angular momentum about the point $O$ is

$A$ particle having mass $4 \ kg$ is moving with velocity $(4 \hat{i} + 2 \hat{j}) \ m/s$. Find the angular momentum of the particle about the origin when it is at position $(1, 1, 0) \ m$.