Intersection of 2 lines

  • Thread starter totototo
  • Start date
  • #1
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Hi;
First i you read my problem and feel that it does not belong to this forum please inform me which one is the right one.

I have 2 lines L1,L2 in 3-dimensions
L1 has (x1,y1,z1) (x2,y2,z2)
L2 has (x3,y3,z3) (x4,y4,z4)
How can I know that these two lines are intersected?

Thanks
toto
 

Answers and Replies

  • #3
HallsofIvy
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Parametric equations for a line through (x1,y1,z1) and (x2,y2,z2) is
x= x1+ (x2-x1)t, y= y1+ (y2-y1)t, z= z1+ (z2-z1)t

Parametric equations for a line through (x3,y3,z3) and (x4,y4,z4) is
x= x3+ (x4-x3)s, y= y3+(y4- y3)s, z= z3+ (z4-z3)s

Set x= x, y= y, z= z to get three equations for s and t. Solve two of the equations for s and t and then see if those values satisfy the third.
 
  • #4
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Thanks alot
 

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