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Math Help - Intersecting planes

  1. #1
    Member Veronica1999's Avatar
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    Intersecting planes

    1. The planes -x+2y+3z=4 and 2x+3y-z=4 intersect to form a line. Find an equation for the line.

    I found two points that satisfy both equations.
    (1,1,1) (2, 6/11, 18/11)

    The equation is x-1 / 1 = y-2 / -5/11 = z-1 / 7/11

    Is it correct?

    2. To the nearest tenth of a degree, find the size of the acute dihedral angle formed by the intersecting planes. Hmmm....

    I have an approach but I am not sure if it will work.

    The perpendicular vector of the plane -x+2y +3z = 4 is
    (-1, 2, 3) and the perpendicular vector for the plane 2x+3y-z=4 is (2, 3, -1)

    cos(x) = 1/14
    x=85.9

    I think I read somewhere that you use the dot product of the perpendicular vectors
    of a plane to get the dihedral angle.... ?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Intersecting planes

    They're both fine! And yes the angle \theta between two planes with normal vectors (x_1,y_1,z_1) and (x_2,y_2,z_2) can be calculated as:
    \theta=\arccos\left(\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}}\right)
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  3. #3
    Member Veronica1999's Avatar
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    Re: Intersecting planes

    Thank You.
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