§ 20: 20.21

20.21 Знайдіть кут між векторами a = m – n і b = m + 2n, якщо |m| = 1, |n| = 3, ∠(m, n) = 30°

a = m – n; b = m + 2n; |m| = 1, |n| = 3.

∠(m, n) = 30°; ∠(a, b) – ?

cos ∠ (a, b) = a • ba|b|

a • b = (m – n)(m + 2n) = m² + 2m n – 2n² = 1 + 1 • 3 • 32 –2 •3 = 1 + 32 – 6 = –3,5.

|a| = m2- 2mn+ n2 = 1-2 •1 • 3 • 32+ 3 = 4-3 = 1.

|b| = m2+ 4mn+ 4n2 = 1+4 •1 • 3 • 32+ 4 •3 =

= 1+6+12 = 19.

cos∠(a, b) = 180° – arccos 71938.