If the points with position vectors `60 hat i+2 hat j , 40 hat i-8 hat j` and `a hat i-52 hat j` are collinear, find the value of `adot`

Explanation

To solve the problem, we need to determine the value of \( a \) such that the points with position vectors \( 60 \hat{i} + 2 \hat{j} \), \( 40 \hat{i} - 8 \hat{j} \), and \( a \hat{i} - 52 \hat{j} \) are collinear.

### Step-by-Step Solution:

1. **Identify the Position Vectors**:
- Let \( P \) be the point with position vector \( \vec{P} = 60 \hat{i} + 2 \hat{j} \).
- Let \( Q \) be the point with position vector \( \vec{Q} = 40 \hat{i} - 8 \hat{j} \).
- Let \( R \) be the point with position vector \( \vec{R} = a \hat{i} - 52 \hat{j} \).
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