|a| = 8 |b| = 12 |a+b| = 4 akar 3 Maka |a-b| = ...

Mapel : Matematika
Kelas : X SMA
Bab : Vektor

Pembahasan :
|a + b|² = |a|² + 2|a| |b| cos θ + |b|²
(4√3)² = 8² + 2(8)(12) Cos θ + 12²
48 = 64 + 144 + 192 Cos θ
Cos θ = - 160/192
Cos θ = - 5/6

Maka...
|a - b|² = |a|² - 2|a| |b| Cos θ + |b|²
|a - b|² = 8² - 2(8)(12) (-5/6) + 12²
|a - b|² = 64 + 160 + 144
|a - b|² = 368
|a - b| = √368
|a - b| = 4√23