x-axis is the intersection of two planes

Options

A. xy and yz
B. yz and zx
C. second octant
D. eithth octant

Answer

To determine which two planes intersect to form the x-axis, we can analyze the equations of the planes involved.

### Step-by-Step Solution:

1. **Understanding the Axes**:
- The x-axis is represented by the coordinates where y and z are both equal to zero. In Cartesian coordinates, any point on the x-axis can be represented as (x, 0, 0).

2. **Identifying the Planes**:
- The **xy-plane** is defined by the equation z = 0. This means that for any point on the xy-plane, the z-coordinate is always zero.
- The **zx-plane** is defined by the equation y = 0. This means that for any point on the zx-plane, the y-coordinate is always zero.

3. **Finding the Intersection**:
- The intersection of the xy-plane (z = 0) and the zx-plane (y = 0) occurs where both conditions are satisfied simultaneously.
- Setting y = 0 and z = 0 gives us the coordinates (x, 0, 0), which corresponds to all points on the x-axis.

4. **Conclusion**:
- Therefore, the x-axis is the intersection of the xy-plane and the zx-plane.

### Final Answer:
The x-axis is the intersection of the **xy-plane** and the **zx-plane**.