The position of a particle is given by: r = (i + 2j – k ) and momentum P = (3i + 4j – 2k ). The angular momentum is perpendicular to

Q: The position of a particle is given by: $ \vec{r} = (\hat{i} + 2\hat{j} – \hat{k} ) $ and momentum $ \vec{P} = (3\hat{i} + 4\hat{j} – 2\hat{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

Ans: (a)

Sol: Angular Momentum , $\vec{L} = \vec{r} \times \vec{P} $

$\vec{L} = (\hat{i} + 2\hat{j} – \hat{k} ) \times (3\hat{i} + 4\hat{j} – 2\hat{k} ) $

$ = -\hat{j} – 2 \hat{k}$