Cross product
← Back: Dot product  Overview: Vector algebra  Next: Matrices → 


The cross product of two vectors is denoted with an . The cross product of vector and vector results in a new vector
that is perpendicular to the surface spanned by vectors and (see figure). Furthermore the three vectors , and build a rectangular coordinate system based on the righthand rule. The magnitude of vector equals the area of the parallelogram spanned by and and is calculated as follows:
In this equation denotes the angle between the two vectors which ranges from to (see figure above). Furthermore it should be noted that the cross product is exclusively defined for the threedimensional euclidian vector space. Therefore the following computational relationship holds:
Based on the described relationships it can be seen, that the commutative law does not hold for the cross product. Instead, the following holds:
Furthermore there are some special cases that lead to simplifications in technical context:
Multimedial educational material
http://demonstrations.wolfram.com/CrossProductOfVectorsInTheYZPlane/ Applet: Cross product of two vectors in the yzplane 
Literature
 Manfred Albach, Grundlagen der Elektrotechnik 1: Erfahrungssätze, Bauelemente, Gleichstromschaltungen, 3. Edition (Pearson Studium, 2011)
 Kurt Meyberg und Peter Vachenauer, Höhere Mathematik 1: Differential und Integralrechnung. Vektor und Matrizenrechnung, 6. Edition (Springer Berlin Heidelberg, 2001)
 Wolfgang Pavel und Ralf Winkler, Mathematik für Naturwissenschaftler, 1. Edition (Pearson Studium, 2007)