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Math Help - Hyperplanes

  1. #1
    Member aldrincabrera's Avatar
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    Smile Hyperplanes

    ,.good day,.,.can anyone please help me with this??

    find the equation of the hyperplane in 4space which goes through the point P= (0,1,-2,3) perpendicular to the vector a= (4,3,1,-2).

    our teacher never explained this and he said this was easy,.,but i am really having a hard time with this,.,thnx,.,
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by aldrincabrera View Post
    ,.good day,.,.can anyone please help me with this??

    find the equation of the hyperplane in 4space which goes through the point P= (0,1,-2,3) perpendicular to the vector a= (4,3,1,-2).

    our teacher never explained this and he said this was easy,.,but i am really having a hard time with this,.,thnx,.,
    The equation of the hyperplane perpendicular to the vector a=(4,3,1,-2) is 4x+3y+z-2t=C

    Use the fact that it passes through the point P to find C.
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  3. #3
    Member aldrincabrera's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by alexmahone View Post
    The equation of the hyperplane perpendicular to the vector a=(4,3,1,-2) is 4x+3y+z-2t=C

    Use the fact that it passes through the point P to find C.


    ,.,.thnx so much,.,ammm,.,.can u please show me a sample of how i shud solve it???i'm really hanging,.,.thnx
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by aldrincabrera View Post
    ,.,.thnx so much,.,ammm,.,.can u please show me a sample of how i shud solve it???i'm really hanging,.,.thnx
    Just substitute the coordinates of P into the equation of the hyperplane.
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  5. #5
    Member aldrincabrera's Avatar
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    Re: Hyperplanes

    ,,.im sorry,.,.but how shud i substitute P to the equation of the hyperplane if my problem is to find for the equation of the hyperplane???
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  6. #6
    MHF Contributor alexmahone's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by aldrincabrera View Post
    ,,.im sorry,.,.but how shud i substitute P to the equation of the hyperplane if my problem is to find for the equation of the hyperplane???
    The equation of the hyperplane is 4x+3y+z-2t=C. Find C by substituting the coordinates of P (0,1,-2,3) into this equation.
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  7. #7
    Member aldrincabrera's Avatar
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    Re: Hyperplanes

    ,.,.owh i get it now,.,.so C is just a number then???ammm.,.then what'll i do with C after i have it??
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  8. #8
    MHF Contributor alexmahone's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by aldrincabrera View Post
    ,.,.owh i get it now,.,.so C is just a number then???ammm.,.then what'll i do with C after i have it??
    Then you will be able to write the equation of the hyperplane as 4x+3y+z-2t=a number
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  9. #9
    Member aldrincabrera's Avatar
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    Re: Hyperplanes

    ,.,.thnx much,.,.
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  10. #10
    Member aldrincabrera's Avatar
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    Re: Hyperplanes

    ,.,.what if the angle between two hyperplanes is defined as the angle between their normals, are the hyperplanes 3x + 2y + 4z - 2w = 5 and 2x - 4y + z + w = 6 orthogonal??
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  11. #11
    MHF Contributor alexmahone's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by aldrincabrera View Post
    ,.,.what if the angle between two hyperplanes is defined as the angle between their normals, are the hyperplanes 3x + 2y + 4z - 2w = 5 and 2x - 4y + z + w = 6 orthogonal??
    The normals are (3,2,4,-2) and (2,-4,1,1) respectively. Can you find the dot product?
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  12. #12
    Member aldrincabrera's Avatar
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    Re: Hyperplanes

    is it 0???
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  13. #13
    MHF Contributor alexmahone's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by aldrincabrera View Post
    is it 0???
    Yes. So the hyperplanes are orthogonal.
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  14. #14
    Member aldrincabrera's Avatar
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    Re: Hyperplanes

    ,.,.thnx so much,.,.ammm,.,.can i ask another question???
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  15. #15
    MHF Contributor alexmahone's Avatar
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    Re: Hyperplanes

    Quote Originally Posted by aldrincabrera View Post
    ,.,.thnx so much,.,.ammm,.,.can i ask another question???
    Sure! Post it in a new thread, though.
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