请帮忙解决向量题:设a,b,c为单位向量,且满足a+b+c=0,求a.b+b.c+c.a
问题描述:
请帮忙解决向量题:设a,b,c为单位向量,且满足a+b+c=0,求a.b+b.c+c.a
答
0=|a+b+c|^2=(a+b+c)*(a+b+c)=3+2(a*b+b*c+c*a),a*b+b*c+c*a=-3/2
请帮忙解决向量题:设a,b,c为单位向量,且满足a+b+c=0,求a.b+b.c+c.a
0=|a+b+c|^2=(a+b+c)*(a+b+c)=3+2(a*b+b*c+c*a),a*b+b*c+c*a=-3/2