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, meaning they lie on the same straight line when their initial point is at (1, 1).

### Step-by-Step Solution:

1. **Identify the terminal points of the vectors**:
- For the vector \( 2\hat{i} + 3\hat{j} \):
- Initial point: \( (1, 1) \)
- Terminal point: \( (1 + 2, 1 + 3) = (3, 4) \)
...