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Math Help - Unit normal vectors

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    Unit normal vectors

    Find a unit normal vector to the surface x+2y+3z at the point (3,0,1)

    How do you normalize the gradient vector?
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    Quote Originally Posted by JJ007 View Post
    Find a unit normal vector to the surface x+2y+3z at the point (3,0,1)

    How do you normalize the gradient vector?
    To normalize ANY vector divide it by its magnitude

    So the normal vector is \vec{v}=\vec{i}+2\vec{j}+3\vec{k}

    Then the unit normal is \vec{n}=\frac{\vec{v}}{||\vec{v}||}=...
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    Quote Originally Posted by TheEmptySet View Post
    To normalize ANY vector divide it by its magnitude

    So the normal vector is \vec{v}=\vec{i}+2\vec{j}+3\vec{k}

    Then the unit normal is \vec{n}=\frac{\vec{v}}{||\vec{v}||}=...
    n=\frac{i+2j+3k}{\sqrt{14}} but what about at point (3,0,1)?
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    Quote Originally Posted by JJ007 View Post
    n=\frac{i+2j+3k}{\sqrt{14}} but what about at point (3,0,1)?
    Find a unit normal vector to the surface x+2y+3z at the point (3,0,1)
    If I understand this correctly you have an equation of a plane

    x+22y+3z=?

    If that is correct planes have the same gradient at every point.
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