Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the angle between two vectors

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data

    A force F =( 6 i - 2 j ) N acts on a particle that under
    goes a displacement D r = ( 3 i + j )m. Find (a) the work done
    by the force on the particle and (b) the angle between F
    and D r .

    2. Relevant equations

    I've found the work to be about 16N. My problem is finding the angle.

    The equation thebook gives is cos(inv)* (Products of vectors A and B) / (A)(i^2+j^2)*(B)(i^2+j^2)

    3. The attempt at a solution

    I used cas(inv)*((VectorA * VectorB) / sqrt(6^2-2^2)(3^2+1^2))

    Which came out to 26 degrees. The back of the book says 36.9 degrees for the answer. I don't think I'm missing anything. All your help is appreciated. Thank you.
  2. jcsd
  3. Sep 23, 2011 #2
    The easiest way that i can think of to find the angle between two vectors is the dot product.

    Remember [itex]\vec{A}\cdot\vec{B}=|A||B|Cos(\theta)[/itex]
  4. Sep 23, 2011 #3
    That's what I used, but I still got 26.5 degrees instead of the 36.9.

    I got part a correct (finding the Force on the object) so I don't think I did any previous calculations incorrectly for the numbers I'm using now.
  5. Sep 23, 2011 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The magnitude of vector A is √( 62 + (-2)2 ) = √( 36 + 4 ) .
  6. Sep 24, 2011 #5
    Holy crap.. thank you.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook