A particles has the positions vector $\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}

Question

A particles has the positions vector $\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and the liner momentum $\overrightarrow{\mathrm{p}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$. Its angular momentum about the origin is\

Professor PC Thomas Classes · Answer

Here, $\vec{r}=\hat{i}-2 \hat{j}+\hat{k}, \vec{p}=2 \hat{i}-\hat{j}+\hat{k}$ Angular momentum, $\overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}} 	imes \overrightarrow{\mathrm{p}}$\ $\vec{L}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \ 1 & -2 & 1 \ 2 & -1 & 1\end{array}ight|$\ $=\hat{\mathrm{i}}(-2+1)+\hat{\mathrm{j}}(2-1)+\hat{\mathrm{k}}(-1+4)$\ $=-\hat{i}+\hat{j}+3 \hat{k}$\