How To Find The Intersection Of Two Lines In Space If At All Possible.

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Homework Statement


I am given the equation of two lines that are in three space. They are in the form of (X=, Y=, Z= ). The questions wants me to prove whether or not the lines intersect.


Homework Equations


The equations of the lines. It gives me just the points in the equation, but it is assumed I can get the equation of the line easily.


The Attempt at a Solution


I guess I need to find a common point some how? I know the intersections may not be at the same time.
 

Answers and Replies

  • #2
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Homework Statement


I am given the equation of two lines that are in three space. They are in the form of (X=, Y=, Z= ). The questions wants me to prove whether or not the lines intersect.


Homework Equations


The equations of the lines. It gives me just the points in the equation, but it is assumed I can get the equation of the line easily.


The Attempt at a Solution


I guess I need to find a common point some how? I know the intersections may not be at the same time.
Use a different parameter for each line. Instead of using t as the parameter for both lines, use, say, s for one line, and t for the other. At any point of intersection both x values have to be equal, both y values, and both z values.
 
  • #3
HallsofIvy
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Note that this will give you three equations (for x, y, and z) in the two unknowns s and t. You can use any two equations to solve for s and t and then you will have to check to see if they satisfy the third. That is why the "general" situation is that two lines in three space do NOT intersect.
 

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