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Point of intersection of two lines

  • Thread starter dcramps
  • Start date
  • #1
43
0

Homework Statement


Find the point of intersection of two lines
x = -9 + 5t
y = 1 + t
z = 10 - 4t

and

x = -2 -3t
y = 5 + 2t
z = 5 + 3t


Homework Equations


N/A


The Attempt at a Solution


I have read that you should set two of the equations equal to find the value of t, and that value of t should hold for the third equation, but whenever I do that I get two different values for t, and neither of them hold up in the third equation. What am I doing wrong?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
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Hi dcramps! :smile:

Where the two lines intersect, the parameter t will be different on each line. :wink:

So call the parameter for the second line u, then set two of the equations equal to find the values of t and u. :smile:
 
  • #3
43
0
Thanks! Now I have my t and u values, and plugging them into the third equation gives me equality...but where do I go from here? Do I plug them into all of the original equations and use the results as my intersection point?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
249
Yup! :biggrin:
 
  • #5
43
0
Excellent. Thanks for your help :)
 

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