Show that the points (-2,4,1),(-1,5,5),(2,2,5) and (1,1,1) are the vertices of a square.

Explanation

To show that the points A(-2, 4, 1), B(-1, 5, 5), C(2, 2, 5), and D(1, 1, 1) are the vertices of a square, we need to follow these steps:

### Step 1: Calculate the distances between the points
We will calculate the lengths of the sides AB, BC, CD, and DA, as well as the diagonals AC and BD.

1. **Distance AB**:
\[
AB = \sqrt{(-1 - (-2))^2 + (5 - 4)^2 + (5 - 1)^2}
...