My Math Forum Calculating intersecting lines in 3D

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 April 23rd, 2014, 09:16 AM #1 Newbie     Joined: Apr 2014 From: Netherlands Posts: 2 Thanks: 0 Calculating intersecting lines in 3D Hello, I am trying to calculate if two lines intersect in 3D, and where the intersecting point is. Now I found this on the internet, but I do not understand everything they explain. linear algebra - Find intersection of two 3D lines - Mathematics Stack Exchange In the answer of robjohn with the colored text, I understand that X stands for Crossproduct. But I do not understand the constant part and how he comes up with the number 400. (As far as I know a constant is a variable that does not change, I do not understand how he gets this 400 out of a vector in this situation) Also I do not understand how t becomes 1/4 in this part: 600−800t=400 t=1/4 Is there anyone who can explain me how this works? Thanks in advance Alexander
 April 24th, 2014, 12:21 AM #2 Newbie     Joined: Apr 2014 From: Netherlands Posts: 2 Thanks: 0 I do understand how t=1/4, it was late yesterday when I posted this. but I still do not get where the 400 comes from.
May 4th, 2014, 11:37 AM   #3
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Every point on the line can be written as $\displaystyle (5,5,4)-t.[(5,5,4)-(10,10,6)]$ So when you multiply $\displaystyle (-20,20,0)$ which is perpendicular to $\displaystyle (5,5,2)$ it is always is equal to constant since t term cancels out....Now assuming you got the 'constant' concept.
Quote:
 400 is nothing but $\displaystyle (-40,-40,200).(5,5,4)$

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