A parallelopiped is formed by planes drawn through the points (1, 2, 3) and
(6, 8, 18) parallel to the coordinate planes then which of the following is not
the length of an edge of the rectangular
parallelpiped

Options

A. (a)5 units
B. (b)10 units
C. (c)15 units
D. (d)6 units

Answer

To solve the problem, we need to determine the lengths of the edges of a rectangular parallelepiped formed by planes through the points (1, 2, 3) and (6, 8, 18) that are parallel to the coordinate planes.

### Step-by-step Solution:

1. **Identify the Points**:
We have two points:
- Point A: (1, 2, 3)
- Point B: (6, 8, 18)

2. **Calculate the Length of the Edge along the x-axis**:
The length along the x-axis is calculated by taking the difference of the x-coordinates of points A and B.
\[ \text{Length along x-axis} = x_2 - x_1 = 6 - 1 = 5 \]

3. **Calculate the Length of the Edge along the y-axis**:
The length along the y-axis is calculated by taking the difference of the y-coordinates of points A and B.
\[ \text{Length along y-axis} = y_2 - y_1 = 8 - 2 = 6 \]

4. **Calculate the Length of the Edge along the z-axis**:
The length along the z-axis is calculated by taking the difference of the z-coordinates of points A and B.
\[ \text{Length along z-axis} = z_2 - z_1 = 18 - 3 = 15 \]

5. **List the Lengths of the Edges**:
Now we have the lengths of the edges of the parallelepiped:
- Length along x-axis: 5
- Length along y-axis: 6
- Length along z-axis: 15

6. **Identify which option is not a length of the edge**:
Given the options (not specified in the question), we need to check which of the provided options is not equal to 5, 6, or 15.
If one of the options is 10, then it is not a length of the edge of the parallelepiped.

### Conclusion:
The length that is **not** an edge of the rectangular parallelepiped is **10**.