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Calc problem r(t)

  1. Oct 9, 2003 #1
    The curves r1(t)=<t,t^2,t^3> and r2(t)=<sin t, sin 2t, t> intersect at the origin. Find their angle (acute) of interesection correct to the nearest degree. (Think! What angle are you trying to locate? Now dn't go off on a tangent.)

    So thats the problem.
    All I got so far is
    r2(t)=sint(i)+sin 2t(j)+t(k)

    Now I'm stuck. I'm not sure where to go now.
  2. jcsd
  3. Oct 9, 2003 #2
    They intersect at the origin at t=0. Now, I only know how to find the angle between two straight lines, so I would disregard the hint and take the derivative. You get r1'(t)=<1,2t,3t^2>=<1,0,0> and r2'(t)=<cost,2cos2t,1>=<1,2,1>.
    Now how do you find the angle f between two vectors?
    f=arccos(sqrt(6)/6)=66 degrees
  4. Oct 10, 2003 #3


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    How is that "disregarding" the hint? The purpose of the hint was to direct you to the tangent lines of the curves.
  5. Oct 10, 2003 #4
    I interpreted, "Don't go off on a tangent" to mean "Tangents aren't the way to solve the problem."
  6. Oct 10, 2003 #5
    Great. My answer matched yours.
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