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 distance formula and check if the distance \( AC \) is equal to the sum of distances \( AB + BC \).

### Step 1: Calculate the distance \( AC \)
Using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
For points \( A(0, -1, -7) \) and \( C(6, 5, -13) \):
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