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Math Help - angel of intersection between curves in 3D

  1. #1
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    Smile angel of intersection between curves in 3D

    Ok, the question's like this...

    The curves r1(t)=<t,t^2,t^3> and r2(t)=<sin t, sin 2t, t> intersect at the origin. Find their angle of intersection correct to the nearest degree.

    Please help~it's an urgent...
    Thank you so much!
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  2. #2
    MHF Contributor

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    Quote Originally Posted by violet8804 View Post
    Ok, the question's like this...

    The curves r1(t)=<t,t^2,t^3> and r2(t)=<sin t, sin 2t, t> intersect at the origin. Find their angle of intersection correct to the nearest degree.

    Please help~it's an urgent...
    Thank you so much!
    Ah, yes! The angel of intersection!

    Oh, wait, you mean "angle". That's not nearly as much fun!

    The angle between two curves is the angle between their tangent lines at the point. You can find the tangent of those angles by taking their derivatives.

    Then use tan(\theta- \phi)= \frac{tan(\theta)- tan(\phi)}{1+ tan(\theta)tan(\phi)}.
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