向量既是代数的对象,又是几何的对象,它是沟通代数、几何的一种工具,有着丰富的实际背景。在高中阶段,学生将了解向量丰富的实际背景,理解平面向量及其运算的意义,能用向量语言和方法表示和解决数学和物理中的一些问题,发展运算能力和解决实际问题的能力。一向量法在解析几何中的应用例1,已知A(-1,-1),B(1,3),C(1,5),D(2,7),直线AB与平行于直线CD吗?解:∵AB=[1-(-1),3-(-1)]=(2,4),CD=(2-1,7-5)=(1,2)。又∵2×2-4×1=0,∴AB∥CD。∵AC=[1-(-1),5-(-1)]=(2,6),AB=(2,4),2×4-2×6 Vector is not only an object of algebra, but also a geometric object. It is a tool for communicating algebra and geometry and has rich practical background. In high school, students will understand the vector-rich practical background, understand the meaning of plane vectors and their operations, represent and solve problems in mathematics and physics using vector languages ​​and methods, develop computational skills, and solve practical problems. A vector method in analytic geometry application 1, known A (-1, -1), B (1,3), C (1,5), D (2,7), a straight line AB and parallel to the straight line CD? Solution: ∵AB = [1 - (- 1), 3 - (- 1)] = (2,4), CD = (2-1,7-5) = (1,2). Also ∵ 2 × 2-4 × 1 = 0, ∴AB∥CD. ∵AC = [1 - (- 1), 5 - (- 1)] = (2,6), AB = (2,4), 2 × 4-2 × 6