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Math Help - Equation of plane question.

  1. #1
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    Equation of plane question.

    Its been a little while since I've done these ones and I'm having a little trouble wrapping my head around this one.

    Question:
    Find the equation of the plane perpendicular to the line tangent to r(t)=(3sint)i - (2cost)j + (t)k at t=pi/2.

    Would the normal vector to the plane simply be the above vector? But then would I use (0,0,0) as a point in the plane?
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  2. #2
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    Quote Originally Posted by dmbocci View Post
    Its been a little while since I've done these ones and I'm having a little trouble wrapping my head around this one.

    Question:
    Find the equation of the plane perpendicular to the line tangent to r(t)=(3sint)i - (2cost)j + (t)k at t=pi/2.

    Would the normal vector to the plane simply be the above vector? No.

    But then would I use (0,0,0) as a point in the plane? No.

    The line tangent to \vec{\text{r}}(t) is in the direction of \displaystyle {{d}\over{dt}}\vec{\text{r}}(t).

    Use the position specified by \vec{\text{r}}(\pi/2) as a point in the plane.
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  3. #3
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    Quote Originally Posted by dmbocci View Post
    Its been a little while since I've done these ones and I'm having a little trouble wrapping my head around this one.

    Question:
    Find the equation of the plane perpendicular to the line tangent to r(t)=(3sint)i - (2cost)j + (t)k at t=pi/2.

    Would the normal vector to the plane simply be the above vector? But then would I use (0,0,0) as a point in the plane?
    Dear dmbocci,

    First find the unit tangent vector to the curve.

    \underline{T}=\dfrac{d\underline r}{ds}=\dfrac{d\underline r}{dt}\times\dfrac{dt}{ds}=\dfrac{\underline{r'}(t  )}{\mid\underline{r'}(t)\mid}

    Then find the unit normal using,

    \dfrac{d\underline{T}}{ds}=\kappa\underline N

    The vector equation of the plane perpendicular to the tangent line would then be,

    \left(\underline{R}-\underline{r}\left(\frac{\pi}{2}\right)\right).\un  derline N=0 where \underline R represent the position vector of any point in the plane.

    Hope this helps you to solve the problem.
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  4. #4
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    Thanks guys, great help!
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