When the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ changes sign to $-\vec{r}$,which one of the following vectors will not flip its sign?

Write the $SI$ unit of angular momentum and its dimensional formula.

$A$ particle of mass $0.5\, kg$ is rotating in a circular path of radius $2\, m$ and centripetal force on it is $9\, N$. Its angular momentum (in $J\cdot s$) is:

$A$ particle of mass $2 \ kg$ located at the position $(\hat{i} + \hat{j}) \ m$ has a velocity $2(\hat{i} - \hat{j} + \hat{k}) \ m/s$. Its angular momentum about the $z$-axis in $kg \cdot m^2/s$ is:

The position vector of a $1\,kg$ object is $\overrightarrow{r} = (3\hat{i} - \hat{j})\,m$ and its velocity is $\overrightarrow{v} = (3\hat{j} + \hat{k})\,m/s$. The magnitude of its angular momentum is $\sqrt{x}\,N\cdot m\cdot s$,where $x$ is:

Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side $a$ in free space. At $t = 0$,they are given an initial velocity $\vec{V}_A = V_0 \hat{u}_{AC}, \vec{V}_B = V_0 \hat{u}_{BA}$ and $\vec{V}_C = V_0 \hat{u}_{CB}$. Here,$\hat{u}_{AC}, \hat{u}_{CB}$ and $\hat{u}_{BA}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally,then the magnitude of the net angular momentum of the system about the centroid of the triangle is: