(a) If a line makes $60^\circ$ and $45^\circ$ angles with the positive directions of $x$-axis and $z$-axis respectively, then find the angle that it makes with the positive direction of $y$-axis. Hence, write the direction cosines of the line. \ OR \ (b) Check whether the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 4}{5} = \frac{y - 1}{2} = z$ are skew or not.

Year	Paper Code	Set	Position
CBSE 2022	Series 65-4	Set 1	Question 10
CBSE 2022	Series 65-4	Set 2	Question 8
CBSE 2022	Series 65-4	Set 3	Question 9

• 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)