`A , B , C , D` are any four points, prove that ` vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=0.`

Explanation

To prove that \( \vec{AB} \cdot \vec{CD} + \vec{BC} \cdot \vec{AD} + \vec{CA} \cdot \vec{BD} = 0 \), we will follow these steps:

### Step 1: Define the vectors
Let:
- \( \vec{A} \) be the position vector of point A.
- \( \vec{B} \) be the position vector of point B.
- \( \vec{C} \) be the position vector of point C.
- \( \vec{D} \) be the position vector of point D.
...