diketahui |a|=5 dan |b|=7 serta |a-b|=√109, tentukan sudut antara vektor a dan b

|a - b| = √109
a^2 - 2ab + b^2 = 109
5^2 - 2ab + 7^2 = 109
25 - 2ab + 49 = 109
74 - 2ab = 109
-2ab = 35
ab = -35/2

a.b = |a| . |b| cos a
-35/2 = 5 . 7 cos a
-35/2 = 35 cos a
cos a = -1/2 (Kuadran II dan III)

a = 180 - 60 = 120°
a = 180 + 60 = 240°

|a| = 5, |b| = 7
|a - b| = √109
|a - b|^2 = √109^2
a.a - 2 a.b + b.b = 109
|a|^2 - 2 |a| |b| cos x + |b|^2 = 109
5^2 - 2 . 5 . 7 cos x + 7^2 = 109
25 - 70 cos x + 49 = 109
-70 cos x = 109 - 25 - 49
Cos x = 35/-70 = -1/2
Cos x = cos 120°
x = 120°
Jadi sudut antara vektor a dan b = 120°