设向量a、b、c,满足a+b+c=0,证明axb=bxc=cxa

问题描述:

设向量a、b、c,满足a+b+c=0,证明axb=bxc=cxa

0=a+b+c,c = -a-b.
bxc=bx(-a-b)=-bxa-bxb=-bxa= axb.
cxa=(-a-b)xa=-axa-bxa=-bxa= axb = bxc.