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Finding the unit vector

  1. Mar 1, 2015 #1
    1. The problem statement, all variables and given/known data
    Suppose ##F(x, y, z, u, v) = xy^2 + yz^2 + zu^2 + uv^2 + vx^2 ## Standing at the point ##(1, 1, 1, 1, 1) ## imagine moving in a direction ##\vec w ## where ##\vec w ## is a unit vector. Find the components of a vector ##\vec u ## such that ## D_\vec u F = 0 ##
    Remember ##\vec w ## needs to be unit vector.

    2. Relevant equations
    Directional vector = ##\nabla F \cdotp \vec w ##

    3. The attempt at a solution

    Directional vector = ## <F_x, F_y, F_z, F_u, F_v> \cdotp \vec w = 0 ##
    So ##\nabla F ## and ## \vec w ## are perpendicular.
    If ## \vec w = <a, b,c, d, e> ## then the components of ## \vec w ## must satisfy ##aF_x + bF_y + cF_z + dF_u + eF_v = 0 ##
    To sum it up ## \vec w = <a, b,c, d, e> \frac {1}{|w|} = ## unit vector

    I only got 4/10 points on this question, so I made a mistake somewhere...
     
  2. jcsd
  3. Mar 1, 2015 #2
    Is that all of the work you did? You have everything in implicit form...
    Your vector <a,b,c,d,e> could be any five numbers at this point.

    You need to go more specific
     
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