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Math Help - Plane geometry problem

  1. #1
    Junior Member
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    Plane geometry problem

    Find the equation of plane which contains the line l:\left\{\begin{array}{l} x=t+2 \\y=2t-1\\z=3t+3 \end{array}\right., and makes the angle of 2\pi/3 with the plane \pi:x+3y-z+8=0.

    Actually don't have any idea so I need your help.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Plane geometry problem

    One given you can already use:
    There's given the plane makes the angle \frac{2\pi}{3} with the plane \pi, in general the angle \theta between two planes is given by the formula:
    \cos(\theta)=\frac{x_1\cdot x_2+y_1\cdot y_2+z_1\cdot z_2}{\sqrt{x_1^2+y_1^2+z_1^2}+\sqrt{x_2^2+y_2^2+z_  2^2}}

    Where (x_1,y_1,z_1) and (x_2,y_2,z_2) are the coordinates of the normal vectors of the two planes.
    You know the coordinates of the normal vector of the plane \pi so you can use this given.

    About the line l I have to think about, but the line is given in a parametric presentation so maybe I would try to reform it to a cartesian presentation by for example the substitution, let y=t. But I'm not sure about this.
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