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Math Help - Find the equation of the level surface through (-1,2-1)

  1. #1
    Ant
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    Find the equation of the level surface through (-1,2-1)

    Hi,

    The question is: Find the eq. of the level surface through point p= (1,2,-1) and find the eq of the straight line in R3 which is normal to this surface at p

    Is finding the equation of the level surface to f(x,y,z) = x^2 - y^2 + z^2 at point (-1,2,-1) the same as finding the equation of the tangent plane to the surface at that point?

    Thanks for any help!
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  2. #2
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    Quote Originally Posted by Ant View Post
    The question is: Find the eq. of the level surface through point p= (1,2,-1) and find the eq of the straight line in R3 which is normal to this surface at p

    Is finding the equation of the level surface to f(x,y,z) = x^2 - y^2 + z^2 at point (-1,2,-1) the same as finding the equation of the tangent plane to the surface at that point?
    No it is not. It simply means writing the equation f(x,y,z)=K where K is a constant.

    So in this case we have f(x,y,z)=f(-1,2,-1).
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  3. #3
    Ant
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    So here we have  K = -2 ?
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  4. #4
    Ant
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    I also have that the equation to of the straight line normal to this surface at p is:

    t (2i -4j -2k) where t is a scalar variable.

    Can anyone say if i'm on the right track here? Thanks
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  5. #5
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    Quote Originally Posted by Ant View Post
    I also have that the equation to of the straight line normal to this surface at p is:

    t (2i -4j -2k) where t is a scalar variable.

    Can anyone say if i'm on the right track here? Thanks
    You forgot the point: <-1,2,-1>+t <-2i -4j -2k>
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  6. #6
    Ant
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    Of course! Thanks again
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