JEE Main 2026 — 28 January, Evening Shift — Question 37

$\overrightarrow{\mathrm{r}}=x \hat{\mathrm{i}}+y \hat{\mathrm{j}}+z \hat{\mathrm{k}}$ $\overrightarrow{\mathrm{v}}=\frac{\mathrm{d} \overrightarrow{\mathrm{r}}}{\mathrm{dt}}=\mathrm{v}_{\mathrm{x}} \hat{\mathrm{i}}+\mathrm{v}_{\mathrm{y}} \hat{\mathrm{j}}+\mathrm{v}_{\mathrm{z}} \hat{\mathrm{k}}$ $\overrightarrow{\mathrm{p}}=\mathrm{m} \overrightarrow{\mathrm{v}}$ $\overrightarrow{\mathrm{L}}=\mathrm{m}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{v}})$

$$=(x \hat{i}+y \hat{j}+z \hat{k}) \times m\left(v_{x} \hat{i}+v_{y} \hat{j}+v_{z} \hat{k}\right)$$

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