Prove that the line through `A(0,-1,-1)` and `B(4,5,1)` intersects the line through `C(3,9,4)` and `D(-4,4,4)` .

Explanation

To prove that the line through points \( A(0, -1, -1) \) and \( B(4, 5, 1) \) intersects the line through points \( C(3, 9, 4) \) and \( D(-4, 4, 4) \), we can use the concept of the shortest distance between two lines in three-dimensional geometry. If the shortest distance is zero, it indicates that the lines intersect.

### Step-by-Step Solution:

1. **Find Direction Ratios of Lines AB and CD:**
- For line \( AB \):
- Direction ratios can be calculated as:
\[
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