推 coolbetter33:good轉到二維就容易了 04/18 15:52
推 ericakk :非常感謝!! 04/19 13:39
※ 引述《ericakk (ericakk)》之銘言：
: 空間中兩點 A(0,-7,1) B(3,2,2)
: __ __
: 在x軸上找一點P，使得PA+PB最短，P點是？
: 答案：（15/7,0,0）
minimize
(x^2+7^2+1)^{1/2} + ((x-3)^2+2^2+2^2)^{1/2}
(x^2+50)^{1/2}+((x-3)^2+8)^{1/2}
You can transform this problem to
" A(0,√50), B(3,√8)
Find P on x-axis to make PA+PB minimum."
optical theorem, mirror image of B is C(3,-√8)
AC line (0,√50) + t (-3,(√50 + √8))
intersects x-axis at t = -√50 / (√50 + √8) = -5/(5+2)=-5/7
hence, minimum occurs at x = 15/7
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