平面向量的数量积是平面向量的考查重点,是历年高考命题的热点,其命题的主要视角之一就是通过向量的数量积及其相关运算,探究两个向量的夹角问题.此类问题关键是要注意两向量夹角的取值范围为[0,π],它包括零角、锐角、直角、钝角和平角,以免考虑问题不全导致范围扩大. The number product of plane vector is the focus of plane vector examination, which is the hot spot of the college entrance examination proposition in the past years. One of the main perspectives of its proposition is to explore the angle between two vectors through the number product of vectors and its related operations. It is important to note that the angle between two vectors is in the range [0, π]. It includes zero angle, acute angle, right angle, obtuse angle, and flat angle so as not to cause the problem to be broadened.