Intersection of Lines: Solving for Intersection Point using Equations

[Lagrange21]

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.

 

[Ray Vickson]

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.

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

 

[Jimmy84]

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

3s= 1 +t
2s=2t
2+s=1+3t

 

[HallsofIvy]

Good. Normally, you can solve two equations for two unknown numbers while here you have three equations. Solve the first two equations for s and t. Do those values satisfy the third equation? If so, the two lines intersect at the point given by that s and t.

 

[Lagrange21]

3s= 1 +t
2s=2t
2+s=1+3t

s = t = 1/2

how can I show that the lines intersect?

 

[SammyS]

3s= 1 +t
2s=2t
2+s=1+3t

s = t = 1/2

how can I show that the lines intersect?

Plug the above value for s & t into the following equations for your two lines.

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