The locus of a point for which x=0 is

Options

A. XY - plane
B. YZ -plane
C. ZX- plane
D. none of these

Explanation

To find the locus of a point for which \( x = 0 \), we can analyze the implications of this equation in three-dimensional space.

### Step-by-Step Solution:

1. **Understanding the Coordinate System**:
In a three-dimensional coordinate system, any point is represented by its coordinates \((x, y, z)\). Here, \( x \), \( y \), and \( z \) are the distances from the point to the respective axes.

2. **Setting the Condition**:
The condition given in the question is \( x = 0 \). This means that we are looking for all points where the x-coordinate is zero.

3. **Identifying the Plane**:
When \( x = 0 \), the points can be represented as \((0, y, z)\). This means that for any value of \( y \) and \( z \), the x-coordinate remains zero.

4. **Visualizing the Locus**:
The set of all points \((0, y, z)\) forms a plane in three-dimensional space. This plane is defined by all combinations of \( y \) and \( z \) while keeping \( x \) constant at zero.

5. **Naming the Plane**:
The plane where \( x = 0 \) is known as the **yz-plane**. It extends infinitely in the y and z directions, but does not extend in the x direction since \( x \) is fixed at zero.

6. **Conclusion**:
Thus, the locus of a point for which \( x = 0 \) is the **yz-plane**.

### Final Answer:
The locus of a point for which \( x = 0 \) is the **yz-plane**.