1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    [tex]
    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}|}
    [/tex]

    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.

    So:

    [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]

    So:

    [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

    ehild

    User Avatar
    Homework Helper
    Gold Member

    How do you get |B| from the components?

    ehild
     
  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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook