思路点拨:在向量的运算中,尤其是数量积的运算,善于挖掘题中的隐含条件往 往会使运算简洁,达到事半功倍的效果. 例1　已知a=(3,-1),b=12,32,存在实数k和t,使得x=a+(t2-3)b,y =-ka+tb,且x⊥y,试求:k+t2t的最小值. 分析:题中隐含着“a·b=0”这一条件,由x⊥y得:x·y=0,从中找 Ideas: In the operation of vectors, especially the calculation of the scalar product, the implicit conditions in the excavation of the questions tend to make the operation concise and achieve a multiplier effect. Example 1 It is known that a = (3, -1), b = 12,32, there are real numbers k and t, such that x=a+(t2-3)b,y=-ka+tb, and x⊥y, try to find the minimum value of k+t2t. Analysis: Implicit in the question The condition “a·b=0” is obtained from x⊥y: x·y=0, from which