Angle between two vectors and their negative vectors

Question

Is it true that for any two vectors $\vec{AP}$ and $\vec{BP}$ , the angle between $\vec{AP}$ and $\vec{BP}$ will be the same as the angle between $\vec{PA}$ and $\vec{PB}$ ?

Answer 1

yes, angle between vectors is given as $$\cos\theta=\frac{\vec{AP}\cdot\vec{BP}}{|\vec{AP}||\vec{BP}|}$$ Now if you take negative of both vectors they cancel in the numerator and you have the same value for $\cos\theta$