$7: 43$ 11 of 12 (?) $O A B$ form a triangle. \[ \begin{array}{l} \overrightarrow{O A}=a+2 b \\ \overrightarrow{O B}=3 a+7 b \end{array} \] Express the vector $\overrightarrow{A B}$ in terms of $a$ and/or $b$. Give your answer in its simplest form. The diagram is not drawn to scale. AA hegartymaths.com 己

Step 1 ：Given: \(\overrightarrow{OA} = a + 2b\) and \(\overrightarrow{OB} = 3a + 7b\)

Step 2 ：To find \(\overrightarrow{AB}\), subtract \(\overrightarrow{OA}\) from \(\overrightarrow{OB}\): \(\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}\)

Step 3 ：\(\overrightarrow{AB} = (3a + 7b) - (a + 2b)\)

Step 4 ：\(\overrightarrow{AB} = 2a + 5b\)

Step 5 ：\(\boxed{\overrightarrow{AB} = 2a + 5b}\)