Find the lengths of the edges of the rectangular parallelepiped formed by planes drawn throgh points (1,2,3) and (4,7,6) parallel to the co ordinate planes

Answer

To find the lengths of the edges of the rectangular parallelepiped formed by the planes drawn through the points (1, 2, 3) and (4, 7, 6) parallel to the coordinate planes, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Points**:
Let the points be \( P(1, 2, 3) \) and \( Q(4, 7, 6) \).

2. **Calculate the Length of the Edge Parallel to the X-axis**:
The edge parallel to the X-axis can be found by taking the absolute difference of the x-coordinates of points P and Q.
\[ \text{Length along X-axis} = |x_2 - x_1| = |4 - 1| = 3 \]
Let this length be denoted as \( L = 3 \).

3. **Calculate the Length of the Edge Parallel to the Y-axis**:
The edge parallel to the Y-axis can be found by taking the absolute difference of the y-coordinates of points P and Q.
\[ \text{Length along Y-axis} = |y_2 - y_1| = |7 - 2| = 5 \]
Let this length be denoted as \( B = 5 \).

4. **Calculate the Length of the Edge Parallel to the Z-axis**:
The edge parallel to the Z-axis can be found by taking the absolute difference of the z-coordinates of points P and Q.
\[ \text{Length along Z-axis} = |z_2 - z_1| = |6 - 3| = 3 \]
Let this length be denoted as \( H = 3 \).

5. **Summarize the Lengths**:
We have calculated:
- Length along X-axis (L) = 3
- Length along Y-axis (B) = 5
- Length along Z-axis (H) = 3

### Final Result
The lengths of the edges of the rectangular parallelepiped are:
- Length (L) = 3
- Breadth (B) = 5
- Height (H) = 3