Question

 

Trong không gian Oxyz, cho \(\overrightarrow{a}=\left(-2;2;2\right),\overrightarrow{b}=\left(1;-1;-2\right)\). Côsin của góc giữa hai vectơ \(\overrightarrow{a},\overrightarrow{b}\) bằng

A. \(\dfrac{-2\sqrt{2}}{3}\).                      B. \(\dfrac{2\sqrt{2}}{3}\).                      C. \(\dfrac{\sqrt{2}}{3}\).                      D. \(\dfrac{-\sqrt{2}}{3}\).

Answer 1

\(\cos \left( {\overrightarrow a ;\overrightarrow b } \right) = \frac{{\overrightarrow a .\overrightarrow b }}{{\left| {\overrightarrow a } \right|.\left| {\overrightarrow b } \right|}} = \frac{{\left( { - 2} \right).1 + 2.\left( { - 1} \right) + 2.\left( { - 2} \right)}}{{\sqrt {{{\left( { - 2} \right)}^2} + {2^2} + {2^2} + } .\sqrt {{1^2} + {{\left( { - 1} \right)}^2} + {{\left( { - 2} \right)}^2}} }} = \frac{{ - 2\sqrt 2 }}{3}\)

Chọn A