已知M(2,5) N(3,-2) 点P在直线向量MN上,且满足向量MP的模=3向量PN的模,求P坐标

问题描述:

已知M(2,5) N(3,-2) 点P在直线向量MN上,且满足向量MP的模=3向量PN的模,求P坐标

P点的参数方程:P(t) = M + t(N-M) = (2,5)+ t(1,-7) = (2+t,5-7t)M=P(0),N = P(1)向量MP的模/向量PN的模 = |t|/|1-t| = 3|t| = 3|1-t|因为 PM > PN,所以 P靠近N点些,于是 t > 01.t = 3(1-t) ==> t = 3/4 ==> P =P(3...