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!

Orthogonal vector question

  1. Mar 10, 2014 #1
    1. The problem statement, all variables and given/known data

    vector A = 3U-V
    vector B = U+2V
    U and V are vectors
    |U| = 3|V|
    Given that vector A and vector B are perpendicular vectors, find the angle between vector U and vector V.

    2. Relevant equations

    A*B = |A||B|cos(∠AB)
    A*A = |A|^2

    3. The attempt at a solution

    Since A and B are perpendicular to each other that means that the dot product will equate zero because cos 90 deg = 0.
    So substituting in the vectors I end up with something like

    (3U-V)*(U+2V) = 0 = 3U*U + 5U*V - 2V*V

    Given that any vector dot product itself gives you the magnitude of the vector squared and that we are trying to figure out the angle UV:
    U*U = |U|^2
    U*V = |U||V|cosθ
    V*V = |V|^2
    3U*U + 5U*V - 2V*V = 3|U|^2 + 5|U||V|cosθ - 2|V|^2

    Rearrange: cosθ = (2|V|^2 - 3|U|^2)/(5|U||V|)

    Substitute in |U| = 3|V| and you get -25/15. I can't get the inverse cos of a number greater than 1 and I can't figure out where I went wrong. Any help would be greatly appreciated.
     
  2. jcsd
  3. Mar 10, 2014 #2

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    Deleted - suggestion was wrong.
     
    Last edited: Mar 10, 2014
  4. Mar 10, 2014 #3
    Oh I was trying to figure out what you meant by that, but I see you changed your suggestion. It's a real head scratcher, of all the stuff I've done with vectors, this question should work out the way I did it but nothing seems to yield a realistic result.
     
  5. Mar 10, 2014 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Of course, ##U## and ##V## could also be the zero vector...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Orthogonal vector question
  1. Orthogonal vector (Replies: 7)

Loading...