Question

Найти угол между векторами a= (2; -4), b= (-6; 2).

Answer 1

$cos alpha = frac{ab}{ |a| |b| } \ ab = 2 times ( - 6) - 4 times 2 = - 12 - 8 = - 20 \ |a| = sqrt{ {2}^{2} + {( - 4)}^{2} } = sqrt{4 + 16} = sqrt{20} = 2 sqrt{5} \ |b| = sqrt{ {( - 6)}^{2} + {2}^{2} } = sqrt{36 + 4} = sqrt{40} = 2 sqrt{10} \ cos alpha = frac{ - 20}{2 sqrt{5} times 2 sqrt{10} } = frac{ - 20}{4 times 5 times sqrt{2} } = - frac{1}{ sqrt{2} }$
=> a = 135°.