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Homework Help: Gradient Vector

  1. May 22, 2015 #1
    1. The problem statement, all variables and given/known data
    For [tex]f(x,y)=x^2-xy+y^2[/tex] and the vector [tex]u=i+j[/tex].
    ii)Find two unit vectors such [tex]D_vf=0[/tex]

    2. Relevant equations

    3. The attempt at a solution
    Not sure if relevant but the previous questions were asking for the unit vector u - which I got [tex]\hat{u}=\frac{1}{\sqrt{2}}(i+j)[/tex] for the maximum value of [tex]D_uf[/tex] which was [tex]\sqrt{2}[/tex].
  2. jcsd
  3. May 22, 2015 #2
    The directional derivative is defined as
    [tex]D_{v}f = \nabla f \cdot \mathbf{v}[/tex]
    Your task is to find two vectors [itex]\mathbf{v}[/itex] such that [itex]D_{v}f = 0[/itex].
  4. May 22, 2015 #3


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    Science Advisor

    This problem doesn't have anything to do with the vector "u". Why is that given? [itex]D_vf[/itex] is the dot product of the gradient, [itex]\nabla f[/itex], and a unit vector in the same direction as vector v. Since you want that to be 0, you are looking for two unit vectors perpendicular to [itex]\nabla f[/itex].

    So "u" was used in previous questions?
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