(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.