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问题: 若第一象限内的点A(x,y)落在经过点(6,-2)且方向向量为a=(3,-2)的直线l上,则t=lo

解答:

直线:{x=6+3t;y=-2-2t}--->y=(2/3)(3-x)
xy = (2/3)(3x-x²) = (-2/3)(x-3/2)²+3/2≤3/2
t = log(3/2)_y-log(2/3)_x
 = log(3/2)_y+log(3/2)_x
 = ln(xy)/ln(3/2)
 ≤1.....最大值为1(x=3/2,y=1时)