设a,b都是非零向量,且满足关系式|a-b|=|a+b|,证明a?b=0

设|a|=|b|=|a-b|=m |a-b|²=a²-2a.b+b² m²=2m²-2a.b a.b=m²/2 a.(a+b)=a²+a.b=m²+m²/2=3m²/2 |a+b|²=a²+2a.b+b²=3m² |a+b|=√3m cos=[a.(a+b)]/[|a|*|a+b|]=(3m²/2)