Write the co- ordinate fo the feet of perpendicualrs form the point (a,b,c) on the co- ordinate axes

Answer

To find the coordinates of the feet of the perpendiculars from the point \( (a, b, c) \) to the coordinate axes, we will analyze each axis one by one.

### Step-by-Step Solution:

1. **Foot of the Perpendicular on the X-axis:**
- The X-axis is defined by points where \( y = 0 \) and \( z = 0 \).
- To find the foot of the perpendicular from the point \( (a, b, c) \) to the X-axis, we keep the x-coordinate the same (which is \( a \)) and set the y and z coordinates to zero.
- Therefore, the coordinates of the foot of the perpendicular on the X-axis is \( (a, 0, 0) \).

2. **Foot of the Perpendicular on the Y-axis:**
- The Y-axis is defined by points where \( x = 0 \) and \( z = 0 \).
- To find the foot of the perpendicular from the point \( (a, b, c) \) to the Y-axis, we keep the y-coordinate the same (which is \( b \)) and set the x and z coordinates to zero.
- Therefore, the coordinates of the foot of the perpendicular on the Y-axis is \( (0, b, 0) \).

3. **Foot of the Perpendicular on the Z-axis:**
- The Z-axis is defined by points where \( x = 0 \) and \( y = 0 \).
- To find the foot of the perpendicular from the point \( (a, b, c) \) to the Z-axis, we keep the z-coordinate the same (which is \( c \)) and set the x and y coordinates to zero.
- Therefore, the coordinates of the foot of the perpendicular on the Z-axis is \( (0, 0, c) \).

### Final Coordinates:
- Foot of the perpendicular on the X-axis: \( (a, 0, 0) \)
- Foot of the perpendicular on the Y-axis: \( (0, b, 0) \)
- Foot of the perpendicular on the Z-axis: \( (0, 0, c) \)