When I use cross products to find an angle of 2 vectors as compared to using dot products, I realised that it's wrong.
Using dot products to find angle
===================================
V = (-3, 1, 0)
W = (1,2,0)
Formula: cosΘ = V dot W /( |V||W| )
=> cosΘ = -1 / √50
=> cosΘ = -0.141421
Inverse of cos gives 98.13° which is the correct angle.
Using cross products to find angle
===================================
V = (-3, 1, 0)
W = (1,2,0)
Formula: |VxW| = |V||W|sinΘ
=> sinΘ = |VxW| / |V||W|
=> sinΘ = 7 / √50
=> sinΘ = 0.989949
Inverse of sin gives 81.869898° which is a wrong angle.
But if 180°-81.869898° gives the right answer.
Why is that so? Is it something wrong with the formula?
Please advice, thank you so much for your time.