Given, angle between A and B, θ = 120° The angle between A and – B, α = 180° − θ = 180° − 120° = 60° Now, from diagram the resultant vector of A and −B will be A − B and the angle between A − B and A is denoted by β.
So, angle between A and −B is calculated as, ϕ = 180°− α = 180°− 60° = 120° Now, from parallelogram law of vector addition angle β can becalculated as follows tan‌β=
−B‌sin‌ϕ
−A+(−B‌cos‌ϕ)
=
−B‌sin‌120°
−A−B‌cos‌120°
=
−B
√3
2
−A+
B
2
=
√3B
2A-B
β=tan−1(
√3B
2A−B
) Hence, the angle between vector A and (A - B) is tan−1(