平面向量既是高中数学的知识板块之一,更是一种数学工具,广泛应用于数学解题之中.本文就平面向量与其它知识的交汇,分类例析如下.一、平面向量与函数的交汇例1已知向量a=(x~2,x+1),b=(1-x,p),若函数f(x)=a·b在区间(-1,1)上是增函数,求p的取值范围.解:可得f(x)=(x~2,x+1)·(1-x,p)=x~2(1-x)+(x+1)p=-x~3+x~2+px+p.则f′(x)=-3x~2+2x+p.若f(x)在区间(-1,1)上是增函数,则在 Plane vector is not only one of the high school mathematical knowledge blocks, but also a mathematical tool, which is widely used in solving mathematical problems.In this paper, plane vector and other knowledge intersection, classification as follows: First, the intersection of plane vector and function Example 1 It is known that the function a (x ~ 2, x + 1) and b = (1-x, p) Find the range of p. Solution: We have f (x) = (x ~ 2, x + 1) · (1-x, p) = x ~ 2 (1-x) + (x + 1) p = then f '(x) = - 3x ~ 2 + 2x + p. If f (x) is an increasing function in the interval (-1, 1)