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在向量一章中,探求有关向量位置关系的等价条件是很重要的问题.教材中给出了向量垂直的向量形式和坐标表示,但有时用这两种表示形式做题不能起到简化运算作用,甚至带来麻烦.现给出向量垂直坐标表示的另外一种形式,并通过实例展现其解题的优势.一、知识介绍结论1两非零向量a与b,并设a=(x1,y1),b=(x2,y2),则a与b垂直等价于a·b=0(向量形式),a与b垂直等价于x1x2+y1y2=
In the chapter on vectors, it is very important to explore the equivalent conditions of the vector’s position relationship, and the vectors are given in vectors and coordinate expressions in the vertical direction, but sometimes the problems with these two kinds of representations can not be simplified Function, and even bring trouble.Now give a vertical vector representation of another form of vector, and through examples to show the advantages of solving problems.First, the introduction of knowledge 1 two non-zero vector a and b, and set a = (x1 , y1), b = (x2, y2), then a and b are vertically equivalent to a · b = 0 (in the form of vectors), a and b are vertically equivalent to x1x2 + y1y2 =