In the figure if P is (a,b,c) find the cordinates of A,B,C and D,E,F

Answer

To find the coordinates of points A, B, C, D, E, and F based on the given point P(a, b, c), we can analyze the positions of these points in relation to the axes in a 3D coordinate system.

### Step-by-Step Solution:

1. **Finding Coordinates of Point A:**
- Point A lies on the x-axis.
- On the x-axis, the y-coordinate and z-coordinate are both 0.
- Therefore, the coordinates of point A are:
\[ A = (a, 0, 0) \]

2. **Finding Coordinates of Point B:**
- Point B lies on the y-axis.
- On the y-axis, the x-coordinate and z-coordinate are both 0.
- Therefore, the coordinates of point B are:
\[ B = (0, b, 0) \]

3. **Finding Coordinates of Point C:**
- Point C lies on the z-axis.
- On the z-axis, the x-coordinate and y-coordinate are both 0.
- Therefore, the coordinates of point C are:
\[ C = (0, 0, c) \]

4. **Finding Coordinates of Point D:**
- Point D lies in the XY-plane.
- In the XY-plane, the z-coordinate is 0.
- The x-coordinate is the same as point P, which is a, and the y-coordinate is the same as point P, which is b.
- Therefore, the coordinates of point D are:
\[ D = (a, b, 0) \]

5. **Finding Coordinates of Point E:**
- Point E lies in the YZ-plane.
- In the YZ-plane, the x-coordinate is 0.
- The y-coordinate is the same as point P, which is b, and the z-coordinate is the same as point P, which is c.
- Therefore, the coordinates of point E are:
\[ E = (0, b, c) \]

6. **Finding Coordinates of Point F:**
- Point F lies in the XZ-plane.
- In the XZ-plane, the y-coordinate is 0.
- The x-coordinate is the same as point P, which is a, and the z-coordinate is the same as point P, which is c.
- Therefore, the coordinates of point F are:
\[ F = (a, 0, c) \]

### Summary of Coordinates:
- \( A = (a, 0, 0) \)
- \( B = (0, b, 0) \)
- \( C = (0, 0, c) \)
- \( D = (a, b, 0) \)
- \( E = (0, b, c) \)
- \( F = (a, 0, c) \)