Show that the points (3,4), (-5, 16), (5,1) are collinear.

Explanation

To show that the points \( A(3, 4) \), \( B(-5, 16) \), and \( C(5, 1) \) are collinear, we can use the concept of vectors. We will find the vectors \( \overrightarrow{AB} \) and \( \overrightarrow{BC} \) and check if they are parallel.

### Step 1: Define the position vectors
Let the position vectors of points \( A \), \( B \), and \( C \) be defined as follows:
- \( \vec{A} = 3\hat{i} + 4\hat{j} \)
- \( \vec{B} = -5\hat{i} + 16\hat{j} \)
- \( \vec{C} = 5\hat{i} + 1\hat{j} \)

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