Direction-cosines of y-axis are ................. .

Answer

To find the direction cosines of the y-axis, we need to understand the concept of direction cosines and how they relate to the angles formed with the coordinate axes.

### Step-by-Step Solution:

1. **Understanding Direction Cosines**:
The direction cosines of a line are the cosines of the angles that the line makes with the positive directions of the coordinate axes. These are denoted as \( L \), \( M \), and \( N \) for the x-axis, y-axis, and z-axis respectively.

2. **Identifying Angles**:
- The y-axis is perpendicular to the x-axis, which means the angle \( \alpha \) (angle with the x-axis) is \( 90^\circ \).
- The y-axis is parallel to itself, so the angle \( \beta \) (angle with the y-axis) is \( 0^\circ \).
- The y-axis is perpendicular to the z-axis, so the angle \( \gamma \) (angle with the z-axis) is \( 90^\circ \).

3. **Calculating Direction Cosines**:
The direction cosines are calculated using the following formulas:
- \( L = \cos(\alpha) \)
- \( M = \cos(\beta) \)
- \( N = \cos(\gamma) \)

Substituting the angles we found:
- \( L = \cos(90^\circ) = 0 \)
- \( M = \cos(0^\circ) = 1 \)
- \( N = \cos(90^\circ) = 0 \)

4. **Final Result**:
Therefore, the direction cosines of the y-axis are:
\[ (L, M, N) = (0, 1, 0) \]