Cho có Tính

* Hướng dẫn giải

Ta có:

\({\left| {\overrightarrow a - 5\overrightarrow b } \right|^2}\\ = {\left( {\overrightarrow a - 5\overrightarrow b } \right)^2} = {\overrightarrow a ^2} - 10\overrightarrow a .\overrightarrow b + 25{\overrightarrow b ^2}\\ = {\left| {\overrightarrow a } \right|^2} - 10.\left| {\overrightarrow a } \right|.\left| {\overrightarrow b } \right|.\cos \left( {\overrightarrow a ,\overrightarrow b } \right) + 25{\left| {\overrightarrow b } \right|^2}\\= {4^2} - 10.4.5.\cos {60^0} + {25.5^2} = 541\)

\(\Rightarrow \left| {\overrightarrow a - 5\overrightarrow b } \right| = \sqrt {541} \)