Question

Diketahui vektor a dan vektor b di R2, jika |a| = 5 , |b| = 7 , dan |a+b| =105, tentukan |a-b| !

Answer 1

|a + b| = √105
|a + b|^2 = √105^2
|a|^2 + 2ab + |b|^2 = 105
25 + 2ab + 49 = 105
2ab = 31
|a - b|^2 = |a|^2 - 2ab + |b|^2
|a - b|^2 = 25 - 31 + 49
|a - b|^2 = 43 => |a - b| = √43