平面向量作为一种工具性知识引入到高中教材,给许多平面几何问题的求解带来了巨大的方便,特别是在处理度量、角度、平行、垂直等问题时,平面向量有其独到之处.但同时也因向量的表达形式和运算形式的灵活性,许多学生对于运用向量解题不太习惯,感到无从下手,往往是既花费大量时间又效果甚微.例1(2012年苏州市统测)在梯形ABCD中,AD∥BC,∠ABC=π3,AD=1,BC=2,P是腰AB所在直线上的动点,则 The introduction of plane vector into high school teaching material as a kind of instrumental knowledge brings great convenience to solving many planar geometric problems, especially when dealing with problems of measurement, angle, parallelism and verticality, plane vector has its own uniqueness. But at the same time, due to the flexibility of vector and operation forms, many students find it hard to get rid of problems by using vector solutions, which often takes a lot of time and has little effect.Example 1 ) In the trapezoidal ABCD, AD∥BC, ∠ABC = π3, AD = 1, BC = 2, P is the moving point on the line where the waist AB is located, then