1. Tardigrade
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  4. The position of a particle is given by r = hati+2 hatj- hatk and its linear momentum is given by p = 3 hati+4 hatj-2 hatk . Then its angular momentum, about the origin is perpendicular to

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

KEAMKEAM 2007

Solution:

$ \overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{P}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 2 & -1 \\ 3 & 4 & -2 \\ \end{matrix} \right| $
$ \overrightarrow{L}=\hat{i}(-4+4)-\hat{j}(-2+3)+\hat{k}(4-6) $
$ =-\hat{j}-2\hat{k} $ $ \overrightarrow{L} $
has components along -y axis and $ -z $ axis. The angular momentum is in y-z plane ie, perpendicular to $ x- $ axis