Cho 2 vectơ a, b thỏa mãn: |vecto a| = 4; |vecto b| = 3; |vecto a - vecto b| = 4

Ta có: \(\left| {\overrightarrow a - \overrightarrow b } \right| = 4 \Rightarrow {\left| {\overrightarrow a - \overrightarrow b } \right|^2} = 16\)

⇒\({\overrightarrow a ^2} + {\overrightarrow b ^2} - 2\overrightarrow a \overrightarrow b = 16\)

⇒\[2\overrightarrow a .\overrightarrow b = {\overrightarrow a ^2} + {\overrightarrow b ^2} - 16 = {4^2} + {3^2} - 16 = 9\]

⇒\[\overrightarrow a .\overrightarrow b = \frac{9}{2}\]

Suy ra: \[\cos \left( {\overrightarrow a ,\overrightarrow b } \right) = \frac{{\overrightarrow a .\overrightarrow b }}{{\left| {\overrightarrow a } \right|.\left| {\overrightarrow b } \right|}} = \frac{{\frac{9}{2}}}{{3.4}} = \frac{3}{8}\].