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Math Help - Show that the two planes are neither coincident, parallel, nor distinct?

  1. #1
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    Show that the two planes are neither coincident, parallel, nor distinct?

    I have a question on my homework I don't really understand, and I was wondering if anyone could help me.

    The question is:

    Show that the two planes are neither coincident, parallel, nor distinct. Identify, geometrically, how the planes intersect and determine the angle between the two planes to the nearest degree.

    x + 2y - 4z + 7 = 0
    2x - 2y - 5z + 10 = 0


    If anyone could help me out I'd really appreciate it! Thanks in advance!
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  2. #2
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    Quote Originally Posted by Random-Hero- View Post

    The question is:

    Show that the two planes are neither coincident, parallel, nor distinct. Identify, geometrically, how the planes intersect and determine the angle between the two planes to the nearest degree.

    x + 2y - 4z + 7 = 0
    2x - 2y - 5z + 10 = 0
    Two planes, if they intersect, intersect in a line.
    An equation of a plane has the form
    n_x x + n_y y + n_z z = d
    where \vec n = <n_x,n_y,n_z> is the normal vector to the plane.
    It can be shown that the angle between two planes' normal vector equals the angle between the planes. You can use the dot product
    \vec n_1 \cdot \vec n_2 = |n_1||n_2|cos(\theta)
    I am not sure if you copied the question correctly, as the two planes have different normal vectors so they must be distinct.

    hth
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  3. #3
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    I think the "nor distinct" is really meant to say "parallel and distinct" I think its just a typo.
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