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Angle of intersection between two parametric curves

  1. Jan 25, 2012 #1

    ElijahRockers

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    Gold Member

    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[itex]\cdot[/itex]r2 = |r1||r2|cos[itex]\theta[/itex], 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
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