Define: Quaternion :-)

Defination of Quaternion

Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics, computer vision and crystallographic textureanalysis.^[5] In practical applications, they can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application.

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CrossProduct
 given two 3D vectors U(U1,U2,U3) and V(V1,V2,V3), we can define the cross product CP of U and V as the vector:
  
CP = [ (U2V3 - U3V2),  (U3V1 - U1V3),  (U1V2 - U2V1)]

OR
         |  (U2V3 - U3V2)  | T
CP = |  (U3V1 - U1V3)  |
         |  (U1V2 - U2V1)  |

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Properties:
    The cross product is orthogonal to both U and V..
    The vectors U, V, UxV align with the right hand rule..
    The length of the cross product is equal to the area of the parallelogram defined by U, V.
    
    U x V = (-V) x (U)     ---skew-symmetry
    U x ( V + W) = U x V + U x W
    (tU) x V = t (U x V)

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parallelogram[.perə'lelə.ɡræm]

1. a two-dimensional geometric figure formed of four sides in which bothpairs of opposite sides are parallel and of equal length, and theopposite angles are equal