$7: 43$
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

Answer

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Answer

$\boxed{\overrightarrow{AB} = 2a + 5b}$

Steps

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 ：$\boxed{\overrightarrow{AB} = 2a + 5b}$

$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.AAhegartymaths.com己

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