Question

4.Найдите косинус угла между векторами а(-4; 5) и (2; 1).​

Answer 1

Ответ:

$\displaystyle \cos( \alpha ) = \frac{ \overrightarrow{a} \overrightarrow{b}}{ \overrightarrow{ |a| } | \overrightarrow{b}| }$

$\overrightarrow{a} \overrightarrow{b} = - 4 \times 2 + 5 \times 1 = - 8 + 5 = - 3$

$|\overrightarrow{a}| = \sqrt{ {( - 4)}^{2} + {5}^{2} } = \sqrt{16 + 25} = \sqrt{41}$

$| \overrightarrow{b}| = \sqrt{ {2}^{2} + {1}^{2} } = \sqrt{4 + 1} = \sqrt{5}$

$\cos( \alpha ) = \frac{ - 3}{ \sqrt{41} \times \sqrt{5} } = - \frac{3}{ \sqrt{205} }$