Assertion (A): The lines $L_1: \vec{r} = (\hat{i} + 2\hat{j}) + \lambda(\hat{i} - \hat{j} + \hat{k})$ and $L_2: \vec{r} = (2\hat{i} - \hat{k}) + \mu(\hat{i} + 2\hat{j})$ are skew.

Reason (R): The direction ratios of $L_1$ and $L_2$ are not proportional.

Explanation

1. 01

   A: $(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2) = (\hat{i} - 2\hat{j} - \hat{k}) \cdot (-2\hat{i} + \hat{j} + 3\hat{k}) = -7 \ne 0$, and the lines are not parallel, so A is true.

2. 02

   R is true, but it only rules out parallel lines; lines that are not parallel can still meet, so R does not explain A.