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Thread: Normal form definition

  1. #1
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    Question Normal form definition

    I have two questions about the normal form of a line that I hope someone can help clarify:


    1. When considering the normal form of a line, does this line need to be a line that doesn't cross through the origin? Based on this definition below, it appears that it can't cross the origin, but logically, I don't see why you would have such a restrictive definition

    Normal form definition-screen-shot-2019-10-03-7.10.35-pm.png

    2. In my linear algebra textbook it says that "In R^2, only lines have a normal form, and in R^3 only planes have a normal form." I could theoretically imagine a line in R^3 that has a normal line to it, so then why does it says that in R^3 only planes can have a normal form?
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  2. #2
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    Re: Normal form definition

    1. There's nothing stopping p being the 0 vector.

    2. Consider a point on a line in R^3. You can draw draw an infinite number of "normals" through that point in R^3 space.
    Now consider a line on a plane in R^3. How many normal planes can you draw that pass through the line?
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