a) \(\overrightarrow a .\overrightarrow b = 2.6 + \left( { - 3} \right).4 = 0 \Rightarrow \overrightarrow a \bot \overrightarrow b\) hay \(\left( {\overrightarrow a ,\overrightarrow b } \right) = {90^0}\)
b) \(\overrightarrow a .\overrightarrow b = 3.5 + 2\left( { - 1} \right) = 13\)
\(\begin{array}{l}
\left| {\overrightarrow a } \right| = \sqrt {9 + 4} = \sqrt {13} ,\\ \left| {\overrightarrow b } \right| = \sqrt {25 + 1} = \sqrt {26} .\\
\Rightarrow cos\left( {\overrightarrow a ,\;\overrightarrow b } \right) = \frac{{13}}{{\sqrt {13} .\sqrt {26} }} = \frac{{\sqrt 2 }}{2}.\\
\Rightarrow \left( {\overrightarrow a ,\;\overrightarrow b } \right) = {45^0}.
\end{array}\)
c) \(\overrightarrow a .\overrightarrow b = - 2.3 + \left( { - 2\sqrt 3 } \right).\sqrt 3 = -12\)
\(\begin{array}{l}
\left| {\overrightarrow a } \right| = \sqrt {4 + 12} = 4,\\ \left| {\overrightarrow b } \right| = \sqrt {9 + 3} = 2\sqrt 3 .\\
\Rightarrow cos\left( {\overrightarrow a ,\;\overrightarrow b } \right) = \frac{{ - 12}}{{4.2\sqrt 3 }} = \frac{{ - \sqrt 3 }}{2}.\\
\Rightarrow \left( {\overrightarrow a ,\;\overrightarrow b } \right) = {150^0}.
\end{array}\)
