Question

if a,b,c are three vectors such that a.b=a.c and a x b = a x c, a is not equal to 0, then show that b=c.

Answer 1

1- a×b×cosx=a×c×cosy
b×cosx=c×cosy
2- a×b×sinx=a×c×siny
b× sinx=c×siny

on deviding sinx÷cosx=siny÷cosy
tanx=tany
x=y
cosx=cosy
on putting in 1
b×cosx=c×cosx. [cosx=cosy]
b=c