Question

The position of particle is given by $\overrightarrow{r}=\hat{i}+2\hat{j}-\hat{k}$ and it's linear momentum is given by $\overrightarrow{p}=3\hat{i}+4\hat{j}-2\hat{k}$. Then it's angular momentum about the origin is perpendicular to

• A. $YZ\text{plane}$
• B. $Z\text{axis}$
• C. $Y\text{axis}$
• D. $X\text{axis}$

Answer 1

The correct option is D $X\text{axis}$

We know,
$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}=\left[\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 2& -1\\ 3& 4& -2\end{array}\right]$
$=(-4+4)\hat{i}-(-2+3)\hat{j}+(4-6)\hat{k}$
$=-1\hat{j}-2\hat{k}$

$\overrightarrow{L}$ has components along $Y$ and $Z$ axis but it has no component in $X$ axis.
$\therefore \overrightarrow{L}$ is in $YZ$ plane and perpendicular to $X$ axis