Question

Vektor A & B satu titik tangkap membentuk Sudut Gamma . Jika Vektor A harganya 2 x Vektor B . Hitung besarnya sudut Gamma jika harga mutlak vektor IA+BI = Akar 1/2 . IA-BI

Answer 1

|A + B| = √A^2 + B^2 + 2.A.B.cos α
|A - B| =√A^2 + B^2 - 2.A.B.cos α
|A + B| = √1/2 |A - B|
(|A + B|)/(A - B|) = 1/2
(2B)^2 + B^2 + 2.(2B).B.cos α/(2B)^2 + B^2 - 2.(2B).B.cos α = 1/2
5B^2 + 4B^2.cos α/5B^2 - 4B^2.cos α = 1/2
(5 + 4.cos α)/(5 - 4.cos α) = 1/2
10 + 8.cos α = 5 - 4.cos α
12.cos α = - 5
cos α = - 5/12
α = arc cos (-5/12) = 114,62 derajat