Diketahui |a|=6 |a+b|=2√19 dan |a-b|=2√7 sudut antara vektor a dan b adalah
![]()
|a| = 6
|a + b| = 2√19
|a - b| = 2√7
Persamaan 1
|a + b|² = |a|² + 2ab + |b|²
(2√19)² = |a|² + 2ab + |b|²
76 = |a|² + 2ab + |b|²
76 = 6² + 2ab + |b|²
|b|² + 2ab = 40
Persamaan 2
|a - b|² = |a|² - 2ab + |b|²
(2√7)² = |a|² - 2ab + |b|²
28 = |a|² - 2ab + |b|²
28 = 6² - 2ab + |b|²
|b|² - 2ab = - 8
Eliminasi a dan b
76 = |a|² + 2ab + |b|²
28 = |a|² - 2ab + |b|²
_________________ -
48 = 4ab
ab = 12
Eliminasi 2ab
|b|² + 2ab = 40
|b|² - 2ab = - 8
________________ +
2|b|² = 32
|b|² = 16
|b| = 4
Sudut antara a dan b
ab = |a| . |b| . cos x
12 = 6 × 4 × cos x
12 = 24 × cos x
cos x = 12 / 24
cos x = ½
cos x = 60°
cos x = π/3
[answer.2.content]
