Prove that if A and B are any nonzero vectors and C: lBlA + lAlB, then the angle between A and C has the same measure as the angle between B and C such that A=(a 1 ,a 2 ,a 3 ); B=(b 1 ,b 2 ,b 3 );...

Prove that if A and B are any nonzero vectors and C: lBlA + lAlB, then the angle between A and C has the same measure as the angle between B and C such that A=(a₁,a₂,a₃); B=(b₁,b₂,b₃); IAI=(a₁
²
,a₂
²
,a₃
²
);
IBI=(b₁
²
,b₂
²
,b₃
²
).