Show that the point A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) are collinear.

Explanation

To determine whether the points A(1, -1, 3), B(2, -4, 5), and C(5, -13, 11) are collinear, we will calculate the distances between the points and check if the sum of the distances between two points equals the distance between the third point.

### Step-by-Step Solution:

1. **Calculate the distance between points A and B (AB)**:
The distance formula in three-dimensional space between two points \( P(x_1, y_1, z_1) \) and \( Q(x_2, y_2, z_2) \) is given by:
\[
PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
...