Angular momentum is

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:

$A$ particle of mass $0.01 \ kg$ has a position vector $\vec{r} = (10\hat{i} + 6\hat{j}) \ m$ and moves with a velocity $\vec{v} = 5\hat{i} \ m/s$. Calculate its angular momentum about the origin in $\hat{k} \ J \cdot s$.

$A$ particle starts from the point $(0, 8) \, m$ and moves with a uniform velocity of $\vec{v} = 3 \hat{i} \, m/s$. What is the angular momentum of the particle about the origin after $5 \, s$ (mass of the particle is $1 \, kg$)?

$A$ 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 Earth is assumed to be a sphere of radius $R$ and mass $M$ having a period of rotation $T$. The angular momentum of the Earth about its axis of rotation is