Show that the points `A(1,-2,-8),B(5,0,-2)a n dC(11,3,7)` are collinear, and find the ratio in which `B` divides `A Cdot`

Explanation

To show that the points \( A(1, -2, -8) \), \( B(5, 0, -2) \), and \( C(11, 3, 7) \) are collinear, we will use the concept of vectors. We will find the vectors \( \overrightarrow{AB} \) and \( \overrightarrow{BC} \) and check if they are scalar multiples of each other.

### Step 1: Find the position vectors of points A, B, and C
The position vectors of the points can be represented as:
- \( \vec{A} = 1\hat{i} - 2\hat{j} - 8\hat{k} \)
- \( \vec{B} = 5\hat{i} + 0\hat{j} - 2\hat{k} \)
- \( \vec{C} = 11\hat{i} + 3\hat{j} + 7\hat{k} \)

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