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Math Help - Direction numbers question

  1. #1
    s3a
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    Direction numbers question

    Could someone please tell me how to find the "the set of direction numbers" [1,-1,1]? I get everything else in that question but I don't recall at all how to find these. (Question, solution and answer attached).

    Any help would be greatly appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Direction numbers question-q8.jpg  
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  2. #2
    Behold, the power of SARDINES!
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    Re: Direction numbers question

    The set of "direction numbers" is the direction vector of the equation of the normal line. When they took the gradient of the surface (The partial derivatives), they evaluated them at the point (1,2,1)

    This gives

    \frac{\partial F}{\partial x}\bigg|_{(1,2,1)}= -2, \frac{\partial F}{\partial y}\bigg|_{(1,2,1)}= 2, \frac{\partial F}{\partial z}\bigg|_{(1,2,1)}= -2


    This gives the direction vector -2\mathbf{i}+2\mathbf{j}-2\mathbf{k} Since they all have a commond factor of "2" the direction vector is the same as -\mathbf{i}+\mathbf{j}-\mathbf{k} the coeffiecents give you the "direction numbers"
    Last edited by TheEmptySet; November 21st 2011 at 11:01 AM. Reason: missing minus sign
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  3. #3
    s3a
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    Re: Direction numbers question

    Thanks!

    Just to say though, ∂F/∂z = -2 != 2 but I got the point.
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  4. #4
    Behold, the power of SARDINES!
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    Re: Direction numbers question

    Quote Originally Posted by s3a View Post
    Thanks!

    Just to say though, ∂F/∂z = -2 != 2 but I got the point.
    Thanks I will fix the above. The funny thing is I typed the correct vector after! haha
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