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    What point on the sphere

    x^{2} + y^{2} + z^{2} = 1

    is closest to the point x = 1, y = 2, z = 3?

    How do I find the condition of this to form a lagrange equation to solve this?

    I have thought of this

    F(x,y,z) = x^{2} + y^{2} + z^{2}

    and \lambda = x^{2} + y^{2} + z^{2} -1 = 0

    Forming equation: L(x,y,z) = x^{2} + y^{2} + z^{2} - \lambda(x^{2} + y^{2} + z^{2} -1)

    I don't know how to start it which is the original problem.


    Finally learning Latex



    \mathrm{Thanks}
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    (Original post by mathsRus)
    What point on the sphere

    x^{2} + y^{2} + z^{2} = 1

    is closest to the point x = 1, y = 2, z = 3?

    How do I find the condition of this to form a lagrange equation to solve this?

    I have thought of this

    F(x,y,z) = x^{2} + y^{2} + z^{2}

    and \lambda = x^{2} + y^{2} + z^{2} -1 = 0

    Forming equation: L(x,y,z) = x^{2} + y^{2} + z^{2} - \lambda(x^{2} + y^{2} + z^{2} -1)

    I don't know how to start it which is the original problem.


    Finally learning Latex



    \mathrm{Thanks}
    You want to minimise the distance from the point (x,y,z) to (1,2,3), not just minimise x^{2} + y^{2} + z^{2}
    This is the same as minimising the distance squared from (x,y,z) to (1,2,3).
    Then you simply need to add the constraint x^{2} + y^{2} + z^{2} -1 = 0 in and minimise.
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    (Original post by joostan)
    You want to minimise the distance from the point (x,y,z) to (1,2,3), not just minimise x^{2} + y^{2} + z^{2}
    This is the same as minimising the distance squared from (x,y,z) to (1,2,3).
    Then you simply need to add the constraint x^{2} + y^{2} + z^{2} -1 = 0 in and minimise.
    Could you please elaborate on your first sentence?

    So do I do (x-1)^{2} +  (y-2)^{2} + (z-3)^{2}
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    (Original post by mathsRus)
    Could you please elaborate on your first sentence?

    So do I do (x-1)^{2} +  (y-2)^{2} + (z-3)^{2}
    Yes, that's what you want to minimise.
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    (Original post by ghostwalker)
    Yes, that's what you want to minimise.
    Thanks
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    some examples here too

    http://www.thestudentroom.co.uk/show....php?t=3351861
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    totally off topic but are you good with perturbation theory? really need help.
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    (Original post by cooldudeman)
    totally off topic but are you good with perturbation theory? really need help.
    I have done some perturbation methods for solving non linear ODEs as a postgad but this is almost 30 years ago.
    I would have to relearn that stuff to help you
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    (Original post by TeeEm)
    I have done some perturbation methods for solving non linear ODEs as a postgad but this is almost 30 years ago.
    I would have to relearn that stuff to help you
    ok no worries
 
 
 
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