v1    0.707   0.000   0.707
v2    0.577   0.577   0.577


   Cross product
v7   -0.289   0.866  -0.577

   Reflected vector
v7   -0.267   0.802  -0.535

   Projected vector
v5    0.408  -0.816   0.408

   Rotation Matrix 
r0   -0.707   0.000   0.707
r1    0.408  -0.816   0.408
r2    0.577   0.577   0.577

   Transformed v1 v2
v3    0.000   0.577   0.816
v4    0.000   0.000   1.000

   Transpose Matrix 
r0   -0.707   0.408   0.577
r1    0.000  -0.816   0.577
r2    0.707   0.408   0.577
   Inverse transform
v3    0.707  -0.000   0.707
v4    0.577   0.577   0.577