Write the perpendicular distannce of the point (x,y,z) form three co ordinate planes (x,y,z being positive )

Answer

To find the perpendicular distance of the point (x, y, z) from the three coordinate planes in a three-dimensional space, we can analyze the distances from each plane separately.

### Step-by-step Solution:

1. **Identify the Coordinate Planes**:
- The three coordinate planes in 3D are:
- XY-plane (where z = 0)
- YZ-plane (where x = 0)
- XZ-plane (where y = 0)

2. **Distance from the XY-plane**:
- The perpendicular distance of a point from the XY-plane is simply the z-coordinate of the point.
- Therefore, the distance from the point (x, y, z) to the XY-plane is:
\[ \text{Distance to XY-plane} = |z| \]
- Since we are given that x, y, z are positive, we have:
\[ \text{Distance to XY-plane} = z \]

3. **Distance from the YZ-plane**:
- The perpendicular distance of a point from the YZ-plane is the x-coordinate of the point.
- Thus, the distance from the point (x, y, z) to the YZ-plane is:
\[ \text{Distance to YZ-plane} = |x| \]
- Again, since x is positive, we have:
\[ \text{Distance to YZ-plane} = x \]

4. **Distance from the XZ-plane**:
- The perpendicular distance of a point from the XZ-plane is the y-coordinate of the point.
- Therefore, the distance from the point (x, y, z) to the XZ-plane is:
\[ \text{Distance to XZ-plane} = |y| \]
- Since y is positive, we have:
\[ \text{Distance to XZ-plane} = y \]

### Final Result:
Thus, the perpendicular distances of the point (x, y, z) from the three coordinate planes are:
- Distance to XY-plane: \( z \)
- Distance to YZ-plane: \( x \)
- Distance to XZ-plane: \( y \)