(a) Find the vector equation of the line passing through the point $(2, 1, 3)$ and perpendicular to both the lines $$\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}; \frac{x}{-3} = \frac{y}{2} = \frac{z}{5}.$$ OR (b) The equations of a line are $5x - 3 = 15y + 7 = 3 - 10z$. Write the direction cosines of the line and find the coordinates of a point through which it passes.

Year	Paper Code	Set	Position
CBSE 2023	Series 65-4	Set 1	Question 25
CBSE 2023	Series 65-4	Set 2	Question 22
CBSE 2023	Series 65-4	Set 3	Question 25

• 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)