The equations of the x-axis are

Options

A. `x=0, y=0`
B. `y=0, z=0`
C. `z=0, x=0`
D. `x=0`

Answer

To find the equations of the x-axis in three-dimensional geometry, we need to understand the nature of the x-axis in the Cartesian coordinate system.

### Step-by-Step Solution:

1. **Understanding the Axes**:
- In three-dimensional space, we have three axes: the x-axis, y-axis, and z-axis.
- The x-axis is the line where the y-coordinate and z-coordinate are both zero.

2. **Identifying Points on the x-axis**:
- Any point on the x-axis can be represented as (x, 0, 0) where 'x' can take any real number value.
- This means that for any point on the x-axis, the y-coordinate is always 0 and the z-coordinate is also always 0.

3. **Writing the Equations**:
- From the above understanding, we can conclude that the equations representing the x-axis are:
- \( y = 0 \)
- \( z = 0 \)

4. **Choosing the Correct Option**:
- Now, looking at the given options:
- a) \( x = 0, y = 0 \)
- b) \( y = 0, z = 0 \)
- c) \( z = 0, x = 0 \)
- d) \( x = 0 \)
- The correct option that represents the x-axis is option b) \( y = 0, z = 0 \).

5. **Conclusion**:
- Therefore, the equations of the x-axis are \( y = 0 \) and \( z = 0 \), and the correct option is **b)**.