"向量是数学中的重要的、基本的概念,它既是代数的对象,又是几何的对象.作为代数的对象,向量可以运算;作为几何的对象,向量有方向,可以运算.作为几何对象,向量有方向,可以刻画直线、平面、切线等几何对象;向量有长度,可以刻画长度、面积、体积等几何度量问题.向量由大小方向两个因素确定,大小反映了向量数的特征,方向反映了向量形的特征.因此, Vector is an important and basic concept in mathematics, which is both an algebraic object and a geometric object. As an algebraic object, a vector can be operated; as a geometric object, a vector has directions and can be operated as a geometric object The vectors have directions and can describe geometric objects such as lines, planes, tangents, etc. The length of a vector can describe geometric metrics such as length, area, volume, etc. The vector is determined by the size and direction of the two factors, and the size reflects the characteristics and direction of the vector number Reflects the vector-shaped features.Therefore,