In the following figure, if the coordinates of `P` are `(a,b,c)` then the coordinates of `A,B` and `C` are respectively

Options

A. `(a,0,0),(b,0,0),(c,0,0)`
B. `(a,0,0),(0,b,0),(0,0,c)`
C. `(0,0,a),(0,b,0),(c,0,0)`
D. `(a,b,c),(b,c,a),(c,a,b)`

Explanation

To find the coordinates of points A, B, and C given that point P has coordinates (a, b, c), we can analyze the positions of these points in relation to the axes in a three-dimensional coordinate system.

### Step-by-Step Solution:

1. **Identify the coordinates of point A**:
- Point A lies on the x-axis.
- By definition, any point on the x-axis has a y-coordinate and a z-coordinate of zero.
- Therefore, the coordinates of point A can be expressed as:
\[ A = (a, 0, 0) \]

2. **Identify the coordinates of point B**:
- Point B lies on the y-axis.
- Similarly, any point on the y-axis has an x-coordinate and a z-coordinate of zero.
- Thus, the coordinates of point B are:
\[ B = (0, b, 0) \]

3. **Identify the coordinates of point C**:
- Point C lies on the z-axis.
- Any point on the z-axis has an x-coordinate and a y-coordinate of zero.
- Therefore, the coordinates of point C are:
\[ C = (0, 0, c) \]

### Final Coordinates:
- The coordinates of A, B, and C are:
- \( A = (a, 0, 0) \)
- \( B = (0, b, 0) \)
- \( C = (0, 0, c) \)