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用向量知识来解决平面解析几何中的直线问题,其最大优点是能把几何知识与代数知识充分结合,从而简化计算。由于从直线方程可以直接得出直线的法向量和方向向量,而由法向量或方向向量也可以直接写出直线方程的一次项系数,所以利用直线的一般式方程Ax+By+C=0的法向量(A,B)或方向向量(B,-A),可以将直线方程中的有关问题用向量来解决。一、求直线方程问题例1已知菱形ABCD的顶点A、C在椭圆x2+3y2=4上,对角线BD所在直线斜率为1,直线BD过点(0,1)时,求直线AC方程。
Using vector knowledge to solve the problem of straight line in plane analytic geometry, the biggest advantage is that it can combine the knowledge of geometry and algebra sufficiently to simplify the calculation. Since the normal vector and the direction vector of the straight line can be obtained directly from the straight line equation and the straight line coefficient can be written directly from the normal vector or the direction vector, the straight line equation Ax + By + C = 0 The normal vector (A, B) or direction vector (B, -A) can be solved by using the vector in the equation of the line. First, find a straight line equation problem Example 1 Known rhombus ABCD vertices A, C in the ellipse x2 + 3y2 = 4 on the diagonal line BD where the slope of 1, the straight line BD points (0,1), the line AC equation.