The direction cosines of the y-axis are

The correct option is (0, 1, 0).

To understand why this is the correct answer, let us first define what direction cosines are.
In a three-dimensional Cartesian coordinate system, the direction cosines of a vector or a line are the cosines of the angles it makes with the positive directions of the coordinate axes, namely the x-axis, y-axis, and z-axis. These angles are typically denoted by $\alpha$, $\beta$, and $\gamma$ respectively.

Thus, the direction cosines are given by:
$l=\cos \left(\alpha \right)$
$m=\cos \left(\beta \right)$
$n=\cos \left(\gamma \right)$

Now, let us determine the angles that the positive y-axis makes with the three coordinate axes:
1. The y-axis is perpendicular to the x-axis. Therefore, the angle $\alpha$ between the y-axis and the positive x-axis is 90° (or $\frac{\pi }{2}$ radians).
2. The y-axis is collinear with itself. Therefore, the angle $\beta$ between the y-axis and the positive y-axis is 0° (or 0 radians).
3. The y-axis is perpendicular to the z-axis. Therefore, the angle $\gamma$ between the y-axis and the positive z-axis is 90° (or $\frac{\pi }{2}$ radians).

Next, we calculate the cosines of these angles to find the direction cosines $(l,m,n)$:
$l=\cos (90°)=0$
$m=\cos (0°)=1$
$n=\cos (90°)=0$

Consequently, the direction cosines of the y-axis are represented by the ordered triplet $(l,m,n)$, which is (0, 1, 0).