"向量的投影及数量积定义与关系详解"

The document "千锤百炼第38炼 向量的数量积-数量积的投影定义.doc" explores the concept of vector dot product and its projection. It begins by laying down the fundamental knowledge related to vector projection. Firstly, it defines the value of a directed line segment on an axis, and then extends this concept to the projection of a point onto a line. This establishes the idea that projection is closely associated with perpendicularity. Moving on to vector projection, the document explains that given a vector ar and a line segment br on axis l, the projection of ar onto br and the projection of br onto ar are denoted as 'A B and ''A B respectively. The document defines the value of ''A B as the projection of ar onto br, and ''A B as the projection vector of ar onto br. The relationship between vector projection and the angle between vectors is then examined. It is observed that the sign of the projections is determined by the angle q between the vectors. If q is acute, the projections (whether ar onto br or br onto ar) are positive. On the other hand, if q is a right angle, the projections; This comprehensive exploration of vector dot product and its projection provides a solid understanding of the topic. It is a valuable resource for anyone seeking to delve deeper into this area of mathematics.