Show that the points A(1, 2, 7), B(2, 6, 3) and `C(3, 10 , -1)` are collinear.

Explanation

To show that the points A(1, 2, 7), B(2, 6, 3), and C(3, 10, -1) are collinear, we can use the concept of vectors. Specifically, we will find the vectors AB, BC, and AC, and then check if the sum of the magnitudes of vectors AB and BC equals the magnitude of vector AC.

### Step 1: Find the vector AB
The vector AB can be found by subtracting the coordinates of point A from the coordinates of point B.

\[ \text{Vector } \mathbf{AB} = \mathbf{B} - \mathbf{A} = (2 - 1) \mathbf{i} + (6 - 2) \mathbf{j} + (3 - 7) \mathbf{k} \]
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