Розділ 4. КООРДИНАТИ, ВЕКТОРИ » 16.25
(a ̅,b ̅) = 120°, |a ⃗| = 2, |b ⃗| = 3. Знайдіть: (a ̅,b ̅) = 120°; |a ⃗| = 2; |b ⃗| = 3. 1) a ⃗ • b ⃗ = |a ⃗| |b ⃗| • cos∠(a ̅, b ̅) = 2 • 3 • cos120° = 2 • 3 • (–1/2) = –3. 2) (a ⃗ + b ⃗) • a ⃗ = a ⃗2 + b ⃗ • a ⃗ = 22 – 3 = 1. 3) b ⃗(a ⃗ – b ⃗) = b ̅a ̅ – b ̅2 = –3 – 32 = –3 –9 = –12. 4) a ⃗(2a ⃗ – 3b ⃗) = 2a ⃗2 – 3a ⃗b ̅ = 2 • 4 – 3 • (–3) = 8 + 9 = 17.