Re: [張爸] 求點到線之距離
※ 引述《winter5690 (bbv)》之銘言：
: 各位大大安安
: 想請問一個題目
: find the distance from the point(2,1,3) to the line
: x-1/2 = y/-1= z+1/1.
: 我的作法是: 將x-1/2 = y/-1= z+1/1 寫成2x-y+z-1=0
: (2,1,3)代入,答案為(5/6)^0.5
: 但是正確答案不是這個,想問我是哪邊出錯了?
拜託下次請把數學式寫好, 到底是 (x-1)/2 還是 x-(1/2)?
P(2,1,3)
Q(1+2t,-t,t-1)
PQ = (2t-1,-t-1,t-4)
(2t-1,-t-1,t-4) dot (2,-1,1) = 6t-5 = 0, t= 5/6
PQ = (4/6,-11/6,-19/6)
distance = sqrt(498/36) = sqrt(83/6)
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