A straight line with direction cosines (0,1,0) is

Options

A. Parallel to x-axis
B. Parallel to y-axis
C. Parallel to z-axis
D. Equally inclined to all the axes

Answer

To determine the nature of a straight line with direction cosines (0, 1, 0), we can analyze the given direction cosines step by step.

### 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 with direction cosines (l, m, n), we have:
- l = cos(α), where α is the angle with the x-axis,
- m = cos(β), where β is the angle with the y-axis,
- n = cos(γ), where γ is the angle with the z-axis.

2. **Identifying the Given Direction Cosines**:
The given direction cosines are (0, 1, 0). This means:
- l = 0 (cos(α) = 0) → The line is perpendicular to the x-axis.
- m = 1 (cos(β) = 1) → The line is parallel to the y-axis.
- n = 0 (cos(γ) = 0) → The line is perpendicular to the z-axis.

3. **Interpreting the Direction Cosines**:
Since l = 0, the line does not have any component in the x-direction. Since m = 1, the line moves entirely in the y-direction. Lastly, since n = 0, the line does not have any component in the z-direction.

4. **Conclusion about the Line's Orientation**:
Based on the values of the direction cosines:
- The line is parallel to the y-axis because it has no component in the x or z directions and is fully aligned in the y-direction.

5. **Final Answer**:
Therefore, a straight line with direction cosines (0, 1, 0) is parallel to the y-axis.