# Angle of intersection between two parametric curves

1. ### ElijahRockers

218
1. The problem statement, all variables and given/known data

This is a problem involving parametric equations.

r1= <t,2-t,12+t2>
r2= <6-s,s-4,s2>

At what point do the curves intersect?

Find the angle of intersection, to the nearest degree.

3. The attempt at a solution

I found the point of intersection, (2,0,16). This is when t=2 and s=4.

I found the tangent vectors.
d/dt(r1) = <1,-1,2t>
d/ds(r2) = <-1,1,2s>

I used r1$\cdot$r2 = |r1||r2|cos$\theta$, using the tangent vectors at t=2 and s=4, and solved for theta.. I came up with 23°, but the system tells me I'm wrong. What happened?

EDIT:: Okay.... it seems like I was coming up with a different answer every time. Got it on my last try though. Gotta be more careful... for anyone wondering, the correct answer is 29°

Last edited: Jan 25, 2012