A rectangular parallelopiped is formed by planes drawn through the points `(5,7,9)` and `(2,3,7)` parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is

Options

A. 2
B. 3
C. 4
D. all of these

Explanation

To find the length of an edge of the rectangular parallelepiped formed by the points \( P(5, 7, 9) \) and \( Q(2, 3, 7) \), we will calculate the distances along each coordinate axis (x, y, and z).

### Step-by-Step Solution:

1. **Identify the coordinates of the points:**
- Point \( P = (5, 7, 9) \)
- Point \( Q = (2, 3, 7) \)

2. **Calculate the length along the x-axis:**
- The x-coordinates of points \( P \) and \( Q \) are 5 and 2, respectively.
- Length along the x-axis = \( |5 - 2| = 3 \)

3. **Calculate the length along the y-axis:**
- The y-coordinates of points \( P \) and \( Q \) are 7 and 3, respectively.
- Length along the y-axis = \( |7 - 3| = 4 \)

4. **Calculate the length along the z-axis:**
- The z-coordinates of points \( P \) and \( Q \) are 9 and 7, respectively.
- Length along the z-axis = \( |9 - 7| = 2 \)

5. **Conclusion:**
- The lengths of the edges of the rectangular parallelepiped are 3, 4, and 2 units along the x, y, and z axes, respectively.
- The question asks for the length of an edge, which can refer to any of these lengths.

### Final Answer:
The lengths of the edges are 3 units (x-axis), 4 units (y-axis), and 2 units (z-axis).