The position vectors of radius are $2\hat i + \hat j + \hat k$ and $2\hat i - 3\hat j + \hat k$ while those of linear momentum are $2\hat i + 3\hat j - \hat k.$ Then the angular momentum is
A
$2\hat i - 4\hat k$
B
$4\hat i - 8\hat k$
C
$2\hat i - 4\hat j + 2\hat k$
D
$4\hat i - 8\hat j$
The position vectors of radius are $2\hat i + \hat j + \hat k$ and $2\hat i - 3\hat j + \hat k$ while those of linear momentum are $2\hat i + 3\hat j - \hat k.$ Then the angular momentum is
Radius vector $\vec r = \overrightarrow {{r_2}} - \overrightarrow {{r_1}} = (2\hat i - 3\hat j + \hat k) - (2\hat i +\hat j + \hat k)$
$\vec r = - 4\hat j$
Linear momentum $\overrightarrow p = 2\hat i + 3\hat j - \hat k$
$\vec L = \vec r \times \vec p = ( - 4\hat j) \times (2\hat i + 3\hat j - \hat k)$
$ = \left| {\,\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\0&{ - 4}&0\\2&3&{ - 1}\end{array}\,} \right|$
$ = 4\hat i - 8\hat k$