WHY DOES THE RESULTANT VECTOR AFTER CROSS PRODUCT PERPENDICULAR TO THE VECTORS BEFORE CROSS PRODUCT??

Dear araku

It is the difinition of vector .suppose three unit vector along the 3 axis ,

i ,j,k

according to definition  iXj =k  ,jXk =i  ,kXi =j  and iXi=0 ,jXj=0, kXk=0

now consider any general vector a =a1i + a2j + a3k

   and  b = b1i + b2j + b3k

 now find aXb=c = (a1i + a2j + a3k)X( b1i + b2j + b3k)

                        = (a1b2-a2b1)k + (a2b3-a3b2)i + (a3b1 - a1b3)j

now find a.c

  it will come that a.c=0

so vector c is perpendicular to vector a

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