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Determine whether the two lines l1 : (3,2,3,-1) + t(1,6,1,-1) and l2 : (1,0,1,1) + t(1,-3,-4,2), intersect in R4 , and if so, find the intersection point.

2007-11-21 18:59:42 · 3 answers · asked by Stevo H 1 in Science & Mathematics Mathematics

3 answers

Determine whether the two lines

L1 = (3,2,3,-1) + s(1,6,1,-1) and
L2 = (1,0,1,1) + t(1,-3,-4,2)

intersect in R4. If so, find the intersection point.

I switched the "t" in the equation of the first line to "s" because the two t's were not the same.

Set the equations of the two lines equal to each other.

x = 3 + s = 1 + t
y = 2 + 6s = 0 - 3t
z = 3 + s = 1 - 4t
w = -1 - s = 1 + 2t

x + w = 2 = 2 + 3t
0 = 3t
t = 0

Plug into the equation for x and solve for s.
x = 3 + s = 1 + 0
s = -2

Now check the equations for y and z to see if the solution is consistant across all the variables.

y = 2 + 6s = 0 - 3t
y = 2 + 6(-2) = 0 - 3(0)
-10 ≠ 0

Since it is not consistant for all variables there is no solution. The lines do NOT intersect.

2007-11-22 16:11:43 · answer #1 · answered by Northstar 7 · 0 0

strains meet at: x=2, y=-19, z=8. the technique to get there is shown in the link below (occasion seventy two on internet site 35), that's what I observed to get the respond. you will possibly no longer like it, yet I anticipate you to do the artwork, in case you're particularly useful buying the respond ought no longer be too complicated. out of your question and that might actually assist you commence with relation to the link: For L1: x=4+t, y=-3+8t, z=2-3t For L2: x=2+4s, y=-19-5s, z=8-9s

2016-11-12 09:38:25 · answer #2 · answered by ? 4 · 0 0

try the algorithm at http://www.softsurfer.com/Archive/algorithm_0104/algorithm_0104B.htm

2007-11-22 08:57:53 · answer #3 · answered by RL612 3 · 0 1

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