两向量的数量积具有性质 :(a-b) 2 ≥0 ,当且仅当a =b时上式取“=”号 .以下从几个方面举例说明其应用 .1　证明等式例 1　已知a ,b∈R ,且a· 1-b2 +b· 1-a2 =1,求证a2 +b2 =1.(第三届“希望杯”全国邀请赛试题 )证明　构造向量a=(a ,1-a2 ) ,b= ( 1-b2 ,b) ,则 (a-b) 2 =2 - The scalar product of two vectors has the property: (ab) 2 ≥ 0, if and only if a = b, the above equation takes the “=” sign. The following examples illustrate its application from several aspects. 1 Prove the equation Example 1 Known a ,b∈R ,and a· 1-b2 +b· 1-a2 =1, to verify a2 +b2 =1.(The third “Hope Cup” National Invitational Test) proves that the construction vector a=(a, 1-a2) ), b= ( 1-b2 ,b), then (ab) 2 =2 -