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Math Help - Shortest distance from point to plane

  1. #1
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    Shortest distance from point to plane

    I don't even know where to start on this one.

    "Find the shortest distance from the point (1,0,-2) to the plane x+2y+z=4"
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  2. #2
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    Re: Shortest distance from point to plane

    It's the distance along the normal to the plane, x+2y+z=4.

    Do you know how to find a vector normal to that plane?
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  3. #3
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    Re: Shortest distance from point to plane

    Is it the cross product of the partial derivative of x and partial derivative of y? And then the magnitude of that?
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  4. #4
    MHF Contributor chisigma's Avatar
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    Re: Shortest distance from point to plane

    Quote Originally Posted by esander4 View Post
    I don't even know where to start on this one.

    "Find the shortest distance from the point (1,0,-2) to the plane x+2y+z=4"
    The equation of the plane can be written as...

    z(x,y)= 4-x-2 y (1)

    ... so that the squared distance from the point (1,0,-2) is...

    \delta^{2} (x,y)= (x-1)^{2}+ y^{2} + \{z(x,y)+2\}^{2} (2)

    Now You minimize \delta^{2}(x,y) respect to x and y and the problem is solved...

    Kind regards

    \chi \sigma
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