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Finding perpendicular vector

  1. Aug 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Find a unit vector in the xy plane which is perpendicular to A = (3,5,1).

    2. Relevant equations

    A_x{B_{x}} + A_y{B_{y}} + A_z{B_{z}} = \textbf{A} \cdot \textbf{B}\\\hat{\textbf{A}} = \frac{\textbf{A}}{|\textbf{A}|}

    3. The attempt at a solution

    In order to be perpendicular, AB = 0 since a perpendicular 90 degrees would mean cos(90) = 0, so the entire dot product becomes 0.


    [tex]\textbf{A} \cdot \textbf{B} = 3{B_{x}} + 5{B_{y}} + 1{B_{z}}[/tex]

    But since B doesn't exist on the z plane:

    [tex]\textbf{A} \cdot \textbf{B} = 3{B_{x}} + 5{B_{y}}[/tex]


    [tex]0 = 3{B_{x}} + 5{B_{y}}[/tex]

    Not sure what to do from here. Using:

    [tex]\hat{\textbf{B}} = \frac{\textbf{B}}{|\textbf{B}|}[/tex]

    How would I turn this B vector into a unit vector?
  2. jcsd
  3. Aug 4, 2012 #2


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    Homework Helper

    How do you get |B| from the components?

  4. Aug 4, 2012 #3
    you can take (1/√34)(-5i+3j) as your unit vector.
    edit-or also 5i-3j in place of -5i+3j.
  5. Aug 5, 2012 #4
    If B is a unit vector, then B dotted with B has to be 1. What does this mean in component form?
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