(a) Find the shortest distance between the lines $l_1$ and $l_2$ given by : $l_1 : \vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda (4\hat{i} + 6\hat{j} + 12\hat{k})$ and $l_2 : \vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu (6\hat{i} + 9\hat{j} + 18\hat{k})$ OR (b) Show that the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z}{1}$ intersect. Also, find their point of intersection.

Year	Paper Code	Set	Position
CBSE 2025	Series Other	Set 1	Question 35
CBSE 2025	Series Other	Set 1	Question 33
CBSE 2025	Series Other	Set 1	Question 34

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)