# 3D Vector Inconsistency

1. May 21, 2011

### paulfr

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 ?

2. May 21, 2011

### Staff: Mentor

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?

3. May 21, 2011

### paulfr

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