Question

Найдите угол между векторами: 1) a {-2,5; 2,5} и b {-5; 5}
2) а {-1; 2} и b {6; 3}

Answer 1

1) 2a = {-2,5 × 2; 2,5 × 2} = {-5; 5} = b

∠(a, b) = ∠(2a, b) = ∠(b, b) = 0°

2) $\frac{1}{3}$b = {6 × $\frac{1}{3}$; 3 × $\frac{1}{3}$} = {2; 1}

∠(a, b) = ∠(a, $\frac{1}{3}$b) = ∠({-1; 2}, {2; 1}) = 90°