Đáp án:
$\left| {\overrightarrow a - \overrightarrow b } \right| = \sqrt {19} $
$\left| {2\overrightarrow a + 3\overrightarrow b } \right| = 6$
Giải thích các bước giải:
\(\begin{array}{l}
{\left( {\overrightarrow a - \overrightarrow b } \right)^2} = {\left( {\overrightarrow a } \right)^2} - 2\overrightarrow a .\overrightarrow b + {\left( {\overrightarrow b } \right)^2}\\
= {a^2} + {b^2} - 2\left| {\overrightarrow a } \right|.\left| {\overrightarrow b } \right|\cos \left( {\overrightarrow a ;\overrightarrow b } \right)\\
= {3^2} + {2^2} - 2.3.2\cos {120^0}\\
= 19\\
\Rightarrow \left| {\overrightarrow a - \overrightarrow b } \right| = \sqrt {19} \\
{\left( {2\overrightarrow a + 3\overrightarrow b } \right)^2} = {\left( {2\overrightarrow a } \right)^2} + 2.2\overrightarrow a .3\overrightarrow b + {\left( {3\overrightarrow b } \right)^2}\\
= 4{a^2} + 9{b^2} + 12\left| {\overrightarrow a } \right|.\left| {\overrightarrow b } \right|\cos \left( {\overrightarrow a ;\overrightarrow b } \right)\\
= {4.3^2} + {9.2^2} +12.3.2\cos {120^0}\\
= 36\\
\Rightarrow \left| {2\overrightarrow a + 3\overrightarrow b } \right| = 6
\end{array}\)
