tự luận câu 3 aaaaaa

$\begin{array}{l}
{\left( {\left| {3\overrightarrow a  - \overrightarrow b } \right|} \right)^2} = 9{\left| {\overrightarrow a } \right|^2} + {\left| {\overrightarrow b } \right|^2} - 6\overrightarrow a .\overrightarrow b \\
25 = {\left( {\left| {\overrightarrow a  + 2\overrightarrow b } \right|} \right)^2} = {\left| {\overrightarrow a } \right|^2} + 4{\left| {\overrightarrow b } \right|^2} + 4\overrightarrow a .\overrightarrow b \\
 \Leftrightarrow 25 = {2^2} + {4.3^2} + 4\overrightarrow a .\overrightarrow b \\
 \Rightarrow \overrightarrow a .\overrightarrow b  =  - \dfrac{{15}}{4}\\
 \Rightarrow {\left( {\left| {3\overrightarrow a  - \overrightarrow b } \right|} \right)^2} = 9{\left| {\overrightarrow a } \right|^2} + {\left| {\overrightarrow b } \right|^2} - 6\overrightarrow a .\overrightarrow b  = {9.2^2} + {3^2} - 6.\left( { - \dfrac{{15}}{4}} \right) = \dfrac{{135}}{2}\\
 \Rightarrow \left| {3\overrightarrow a  - \overrightarrow b } \right| = \dfrac{{3\sqrt {30} }}{2}
\end{array}$