Q. The position of a particle is given by: $\overrightarrow{r} = (\widehat{i} + 2\widehat{j} - \widehat{k})$ and momentum $\overrightarrow{P} = (3\widehat{i} + 4\widehat{j} - 2\widehat{k})$. The angular momentum is perpendicular to
A) $X$- axis
B) $Y$- axis
C) $Z$- axis
D) Line at equal angles to all the three axes
Explanation
(a) $\overrightarrow{L} = \overrightarrow{r} \times \overrightarrow{p} = \left| \begin{matrix}
\widehat{i} & \widehat{j} & \widehat{k} \\
1 & 2 & - 1 \\
3 & 4 & - 2
\end{matrix} \right| = - \widehat{j} - 2\widehat{k}$
and the $X -$ axis is given by $\widehat{i} + 0\widehat{j} + 0\widehat{k}$
Dot product of these two vectors is zero $i.e.$ angular momentum is perpendicular to $X -$ axis
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.