3D Vector Inconsistency


by paulfr
Tags: 3d vectors, intersecting, parametric lines
paulfr
paulfr is offline
#1
May21-11, 10:46 AM
P: 175
If I put these 2 lines in to wolframalpha.com it comes up with a solution

x = 1 + 2t , y = 2 – t , z = t ; x = -2 – s , y = 3 + 3s , z = 1 + 4s

t = -8/5 and s = 1/5 using equations for x & y

Solution; x = -11/5 y = 18/5 z = 9/5


But the z values do not match so how can these lines intersect ?

Thanks for your input
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Mark44
Mark44 is offline
#2
May21-11, 11:20 AM
Mentor
P: 20,943
Setting the x, y, and z values equal, you get the system of equations
1 + 2t = -2 - s
2 - t = 3 + 3s
t = 1 + 4s

Moving the variables to one side gives this system
s + 2t = -3
3s + t = -1
4s - t = -1

Using matrix methods, this turns out to be an inconsistent system, meaning that the two lines don't intersect. Are you sure that the equations you entered into wolframalpha are the same as you posted?
paulfr
paulfr is offline
#3
May21-11, 11:41 AM
P: 175
Yes I checked the data several times
Wolframalpha's solution seems to ignore that z=t which
gives a different value than the 9/5 from z=1+4s

Perhaps there is some subtle interpretation they are making ?

The lines appear skew to me

Thanks for the comments


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