Direction-cosines of x-axis are, .............. .

Answer

To find the direction cosines of the x-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Direction Cosines**:
Direction cosines are the cosines of the angles that a line makes with the coordinate axes. For a line making angles \( \alpha \), \( \beta \), and \( \gamma \) with the x-axis, y-axis, and z-axis respectively, the direction cosines are given by:
\[ L = \cos \alpha, \quad M = \cos \beta, \quad N = \cos \gamma \]

2. **Identifying Angles for the x-axis**:
The x-axis is a line that is aligned with the x-direction. Therefore:
- The angle \( \alpha \) (angle with the x-axis) is \( 0^\circ \) because it is parallel to the x-axis.
- The angle \( \beta \) (angle with the y-axis) is \( 90^\circ \) because it is perpendicular to the y-axis.
- The angle \( \gamma \) (angle with the z-axis) is \( 90^\circ \) because it is also perpendicular to the z-axis.

3. **Calculating Direction Cosines**:
Using the angles identified:
- \( L = \cos 0^\circ = 1 \)
- \( M = \cos 90^\circ = 0 \)
- \( N = \cos 90^\circ = 0 \)

4. **Writing the Direction Cosines**:
Therefore, the direction cosines of the x-axis are:
\[ (L, M, N) = (1, 0, 0) \]

### Final Answer:
The direction cosines of the x-axis are \( (1, 0, 0) \).

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