Find the lengths of the medians of the triangle with vertices `A(0,0,6),\ B(0,4,0)a n d\ C(6,0,0)dot`

Explanation

To find the lengths of the medians of the triangle with vertices \( A(0,0,6) \), \( B(0,4,0) \), and \( C(6,0,0) \), we will follow these steps:

### Step 1: Find the midpoints of the sides of the triangle.
The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. We need to find the midpoints of the sides \( BC \), \( AC \), and \( AB \).

1. **Midpoint of \( BC \)**:
\[
M_{BC} = \left( \frac{x_B + x_C}{2}, \frac{y_B + y_C}{2}, \frac{z_B + z_C}{2} \right) = \left( \frac{0 + 6}{2}, \frac{4 + 0}{2}, \frac{0 + 0}{2} \right) = (3, 2, 0)
...