1. **State the problem:** We are given vectors \(\overrightarrow{OA} = 5a + 8b\) and \(\overrightarrow{OB} = 6a - b\) and need to find the vector \(\overrightarrow{AB}\) in terms of \(a\) and \(b\), fully simplified. 2. **Recall the formula:** The vector from point A to point B is given by $$\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}$$ This means we subtract the coordinates of A from those of B. 3. **Substitute the given vectors:** $$\overrightarrow{AB} = (6a - b) - (5a + 8b)$$ 4. **Simplify the expression:** $$\overrightarrow{AB} = 6a - b - 5a - 8b = (6a - 5a) + (-b - 8b) = a - 9b$$ 5. **Final answer:** $$\overrightarrow{AB} = a - 9b$$ This means the vector from A to B is \(a - 9b\).