Help-----proof-----------vecto...

given


A = (a1,a2,a3),B = (b1,b2,b3) , C =(c1,c2,c3)





how to prove


A x ( B x C ) = ( A .C) B - ( A . B )C





*A,B,C are vectors

Help-----proof-----------vecto...
Define V = B x C; clearly V is perpendicular to the plane of B and C.





Thus A x V must be IN the plane of B and C.





Let A x V = λ B + µ C;





Then A . [A x (B X C] = λ A . B + µ A . C


this implies that λ A . B + µ A . C = 0.





This relationship is certainly satisfied by λ = A.C


and µ = - A.B.





We have shown that A x (B x C) = (A.C) B - (A.B) C is a possibility, but my method shows only that


A x (B x C) = p {(A.C) B - (A.B) C} where p is a scalar multiplier.





It should be possible to show that p = 1.

apricot