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Thread: 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
    $\displaystyle n_x x + n_y y + n_z z = d$
    where $\displaystyle \vec n = <n_x,n_y,n_z>$ 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
    $\displaystyle \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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