Prove that the points ( 0,-1,-7) , (2,1,-9) and (6,5,-13) are collinear. Find the ratio in which the frist point divides the join of the other two.

Explanation

To prove that the points \( A(0, -1, -7) \), \( B(2, 1, -9) \), and \( C(6, 5, -13) \) are collinear, we will use the concept of distances between the points. If the sum of the distances between two points equals the distance between the third point and one of those two points, then the three points are collinear.

### Step 1: Calculate the distance \( AB \)

Using the distance formula:
\[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
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