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Math Help - two concepts in double integral.

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    Question two concepts in double integral.

    Can anyone explain to me the following concepts? Thank you very much.

    1) a normal vector to the surface.

    2) a principle unit normal vector to the surface.
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    Quote Originally Posted by kittycat View Post
    Can anyone explain to me the following concepts? Thank you very much.

    1) a normal vector to the surface.

    2) a principle unit normal vector to the surface.
    It means a vector perpendicular (orthogonal) to the surface.
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    Super Member Rebesques's Avatar
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    2) a principle unit normal vector to the surface.
    Alright, if I am getting this right - Say you have a n-dimensional surface in {\mathbb R}^m (certainly m>n). Choose a point on the surface and consider the tangent hyperplane at that point. This has n vectors as basis: x_1,\ldots,x_n. To complete this set to a basis of {\mathbb R}^m, you need m-n linearly independent vectors, orthogonal to that hyperplane: \xi_1,\ldots,\xi_{m-n}. These are called principal normal vectors. Divide by their lengths to get them to be unit: \frac{1}{|\xi_1|}\xi_1,\ldots,\frac{1}{|\xi_{m-n}|}\xi_{m-n}
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