Question

prove a×(b-c) = (a×b)×c

Answer 1

Answer:

Let A=ia1 + ja2 + ka3B= ib1 +jb2 =kb3 andC=ic1 + jc2 +kc3B.C =b1c1 + b2c2 +b3c3 is a scaler and soA.(B.C) = (b1c1 + b2c2 +b3c3)(ia1 +ja2 +ka3)A.(B.C) = ia1b1c1 +ja2b2c2 +ka3b3c3 . . . . . . . . . . .(1)A.B = a1b1 + a2b2 +a3c3 is a scaler and(A.B).C = (a1b1 + a2b2 +a3c3)(ic1 + jc2 +kc3)(A.B).C = ia1b1c1 + ja2b2c2 + ka3b3c3 . . . . . . . . . . (2)RHS’s of (1) and (2) are identical and sothe LHS’s should be equal and hence it follows thatA.(B.C) = (A.B).C