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 lengths of the edges of the rectangular parallelepiped formed by the points (5, 7, 9) and (2, 3, 7), we can follow these steps:

### Step 1: Identify the coordinates of the points
We have two points:
- Point A: (5, 7, 9)
- Point B: (2, 3, 7)

### Step 2: Determine the lengths of the edges
The lengths of the edges of the rectangular parallelepiped can be calculated by taking the absolute difference of the corresponding coordinates of the two points.

1. **Length along the x-axis (a)**:
\[ a = |x_1 - x_2| = |5 - 2| = 3 \]

2. **Length along the y-axis (b)**:
\[ b = |y_1 - y_2| = |7 - 3| = 4 \]

3. **Length along the z-axis (c)**:
\[ c = |z_1 - z_2| = |9 - 7| = 2 \]

### Step 3: Summarize the lengths of the edges
The lengths of the edges of the rectangular parallelepiped are:
- Edge a = 3
- Edge b = 4
- Edge c = 2

### Step 4: Conclusion
Thus, the lengths of the edges of the rectangular parallelepiped formed by the given points are 3, 4, and 2.