Show that there is a very simple method for producing anortho normal frame in R4 whose first vector is any given non null vector (a,b,c,d). Prove that    For any non null quarter nion Z and any two...

Show that there is a very simple method for producing anortho normal frame in R4 whose first vector is any given non null vector (a,b,c,d).

Prove that

For any non null quarter nion Z and any two quaternions X,Y(i.e.,ρZ is an auto mor-phism of H),and that
  for arbitrary quaternions
  for arbitrary quaternions

Investigate the different shapes of the Voronoi diagram for asset of 3 points, and then for asset of 4 points.