The vectors `2i+3 hat j ,5 hat i+6 hat j` and 8` hat i+lambda hat j` have initial points at (1, 1). Find the value of `lambda` so that the vectors terminate on one straight line.

Explanation

To solve the problem, we need to find the value of \( \lambda \) such that the vectors \( 2\hat{i} + 3\hat{j} \), \( 5\hat{i} + 6\hat{j} \), and \( 8\hat{i} + \lambda\hat{j} \) are collinear when they have the same initial point at \( (1, 1) \).

### Step-by-Step Solution:

1. **Identify the Vectors**:
The vectors can be represented as:
- \( \mathbf{A} = 2\hat{i} + 3\hat{j} \)
- \( \mathbf{B} = 5\hat{i} + 6\hat{j} \)
...