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Math Help - Where does the plane intersect the curve?

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    Where does the plane intersect the curve?

    Find the point(s) where the following plane and curve intersect:
    2x+3y-9z=0
    r(t)= <3cost, 3sint, cost> for [0,2pi]
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    Re: Where does the plane intersect the curve?

    Quote Originally Posted by jessicadowning View Post
    Find the point(s) where the following plane and curve intersect:
    2x+3y-9z=0
    r(t)= <3cost, 3sint, cost> for [0,2pi]
    Just plug into the equation for the plane and solve for t!

    6\cos(t)+9\sin(t)-9\cos(t)=0 \iff 9\sin(t)=3\cos(t) \iff \tan(t)=\frac{1}{3}

    Now taking the arctan of both sides gives

    t=\tan^{-1}\left( \frac{1}{3}\right)+\pi n,  n \in \mathbb{Z}

    Now just restric n to get the solutions in the needed interval.
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