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April 23rd, 2014, 10:16 AM   #1
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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
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April 24th, 2014, 01:21 AM   #2
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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.
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May 4th, 2014, 12:37 PM   #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.
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400 is nothing but $\displaystyle (-40,-40,200).(5,5,4)$
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