The discussion revolves around determining whether two lines intersect and finding the intersection point using their parametric equations. The lines are defined by the equations x=1+t, y=2t, z=1+3t and x=3s, y=2s, z=2+s.
Some participants have suggested methods for approaching the problem, including solving pairs of equations for the parameters. There is ongoing exploration of whether the derived values for s and t lead to a valid intersection point.
Participants express uncertainty about how to demonstrate the intersection of the lines and the implications of the equations involved. There is a focus on the relationships between the parameters and the coordinates of the lines.
Lagrange21 said:Homework Statement
Show that these lines intersect and what is the intersection point?
x=1+t
y=2t
z=1+3t
and
x=3s
y=2s
z=2+s
Homework Equations
The Attempt at a Solution
I don't know how to start, some help please.
3s= 1 +tRay Vickson said:You want x,y and z on the first line to equal x,y and z on the second line. What does that tell you?
RGV
Plug the above value for s & t into the following equations for your two lines.Lagrange21 said:3s= 1 +t
2s=2t
2+s=1+3t
s = t = 1/2
how can I show that the lines intersect?
Lagrange21 said:Homework Statement
Show that these lines intersect and what is the intersection point?
x=1+t
y=2t
z=1+3t
and
x=3s
y=2s
z=2+s