# Equations of Lines/Multivariable Calculus

• EngnrMatt

## Homework Statement

Determine whether the lines
L1:x=t, y=16+4t ,z=8+t
and
L2:x=−7+2t, y=−8+6t, z=−3+4t
intersect, are skew, or are parallel. If they intersect, determine the point of intersection

## Homework Equations

t = -7 + 2s

16 + 4t = -8 + 6s

8 + t = -3 + 4s

## The Attempt at a Solution

I solved the first two equations for s and t then plugged them into the third which confirmed that the lines intersect. To determine the point of intersection, I figured that setting the parametric equations equal to each other and solving for t would give the correct answer, but that doesn't seem to be the right way (I got 7 for the x-coordinate of the intersection).

So my question is how do I find the intersection?

Once you found out that the lines interesected by solving for t and s, substituting either t in L1 or s in L2 would give you the point of intersection. They should match up if you do both. (And I'm not sure about 7 for the x-coordinate, double check your math).

Yep, you're right, thanks! It worked.

Sure thing!