anchor.diff:  
   [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}
  +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.
  
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: 
  *_Any 3D rotation is equivalent a unit quaternion stem:[q] that stem:[\left|q\right|=1]._*
  
  ---
  [NOTE, indent=2]
  .Note
  ====
  This claim actually has 2 sides. Let me go a little be more in details in math term: 
  (1). For any 3D rotation equivalent to a rotation angle stem:[θ] along axis stem:[\vec{v}], there exists a unit quaternion stem:[q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})] to describe this rotation. 
  (2). For any unit quaternion stem:[q=(x,y,z,w)], it describes a rotation of angle stem:[θ=2cos^{-1}w] along axis stem:[\vec{v}=\frac{(x,y,z)}{\sqrt{1-w^{2}}}].
  
  ====
  ---
  
  From now on, any quaternion stem:[q] used in this article is by default a unit quaternion, and we will use stem:[q] to describe rotations.
  
  