Homework Help: Intersection of Lines

1. Jul 26, 2012

Lagrange21

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

I don't know how to start, some help please.

2. Jul 26, 2012

Ray Vickson

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

3. Jul 26, 2012

Jimmy84

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

4. Jul 26, 2012

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.

5. Jul 26, 2012

Lagrange21

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

s = t = 1/2

how can I show that the lines intersect?

6. Jul 26, 2012

SammyS

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