anchor.diff:  
   [stem]
   ++++
  -q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})\\
  -=-{q_a}{q_v}\\
  -=-{q_v'}{q_a}
  +q&=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})\\
  +&=-{q_a}{q_v}\\
  +&=-{q_v'}{q_a}
   ++++
   
   This gives stem:[{q_v'}{q_a}={q_a}{q_v}].
  
positive.code: 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
  
negative.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.
  