Question

$\overrightarrow{r} = x\widehat{i} + y\widehat{j} + z\widehat{k}$

$$\begin{matrix} \overrightarrow{v} & \ = \frac{d\overrightarrow{r}}{dt} = v_{x}\widehat{i} + v_{y}\widehat{j} + v_{z}\widehat{k} \\ \overrightarrow{p} & \ = m\overrightarrow{v} \\ \overrightarrow{L} & \ = m(\overrightarrow{r} \times \overrightarrow{v}) \\ & \ = (x\widehat{i} + y\widehat{j} + z\widehat{k}) \times m\left( v_{x}\widehat{i} + v_{y}\widehat{j} + v_{z}\widehat{k} \right) \end{matrix}$$

When sign of $\overrightarrow{r}$ changes, $\overrightarrow{L}$ remains same.