(a) Find the shortest distance between the lines $\frac{x - 8}{3} = \frac{y + 9}{-16} = \frac{z - 10}{7}$ and $\frac{x - 15}{3} = \frac{y - 29}{8} = \frac{z - 5}{-5}$. OR (b) Find the point of intersection of the lines $\vec{r} = \hat{i} - \hat{j} + 6\hat{k} + \lambda(3\hat{i} - \hat{k})$, and $\vec{r} = -3\hat{j} + 3\hat{k} + \mu(\hat{i} + 2\hat{j} - \hat{k})$. Also, find the vector equation of the line passing through the point of intersection of the given lines and perpendicular to both the lines.

Year	Paper Code	Set	Position
CBSE 2024	Series Other	Set 1	Question 35
CBSE 2024	Series Other	Set 1	Question 34
CBSE 2024	Series Other	Set 1	Question 33

• 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)