Vector Algebra

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(

√3B

2A−B

).