How cross product is defined in n-dimensional vector space.this is asked by g. sudhakaran.his e-mai id is sudhakaranghotmail.com?

Answer 1

The cross product in n-dimensional vector space is the non-diagonal lements of the matrix created by the multiplicationof the two n-dimensional vectors. For example:

A= a1 + a2 + a3 + a4 and B= b1 + b2 + b3 + b4 where A and B are vectors, then the cross product is simply the square multiplication table product minus the diagonal terms:

AXB=

b1 b2 b3 b4

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a1| a1b2 a1b3 a1b4

a2| a2b1 a2b3 a2b4

a3| a3b1 a3b2 a3b4

a4| a4b1 a4b2 a4b3

The cross product here is :

(a1b2-a2b1) + (a1b3 - a3b1) + (a1b4 - a4b1) + (a2b3 -a3b2) + (a2b4-a4b2) + (a3b4-a4b3)