anchor.diff:  It becomes harder to visualize stem:[\vec{a}] and stem:[\vec{b}] if we go this way, and the negative sign does not really introduce a lot of difficulties, so we will stick with that negative sign in this article.
   
   ====
  +---
   
   
   === Flip Vector
  
positive.code: 
  [stem]
  ++++
  q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})\\
  =(\vec{a}×\vec{b},\vec{a}·\vec{b})\\
  =-(-\vec{a}×\vec{b},-\vec{a}·\vec{b})\\
  =(\vec{b}×\vec{a},-\vec{a}·\vec{b})\\
  =-{q_b}{q_a}
  ++++
  
  Here you can also clearly see why we are using stem:[sin⁡\frac{θ}{2}] and stem:[cos⁡\frac{θ}{2}] in quaternions.
  
negative.code: 
  [stem]
  ++++
  -q&=(-sin⁡\frac{θ}{2}\vec{v},-cos⁡\frac{θ}{2})\\
  &=(-sin⁡\frac{2π-θ}{2}\vec{v},cos⁡\frac{2π-θ}{2})\\
  &=(sin⁡\frac{-(2π-θ)}{2}\vec{v},cos⁡\frac{-(2π-θ)}{2})\\
  ++++
  
  Recall that stem:[sin⁡θ=sin(π-θ)] and stem:[-cos⁡θ=cos(π-θ)], then stem:[-sin⁡θ=sin(-θ)] and stem:[cos⁡θ=cos(-θ)].
  