1. Limited time only! Sign up for a free 30min personal 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!

Proof of Cosine law using vectors

  1. Mar 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Two vectors of lengths a and b make an angle θ with each other when placed tail to tail. Prove, by taking components along two perpendicular axes, that the length of the resultant vector is r=√(a^2+b^2+2abcos θ )

    2. Relevant equations

    Would this be correct?
    How would you simplify it?:uhh:


    3. The attempt at a solution
    So ax = acos θ , bx = bcos θ , ay = asin θ , by = bsin θ. So rx = ax + bx and ry = ay + by . So r=√(r_x+r_y ) .
    Which means that, √(〖[(a+b)cosθ]〗^2+〖[(a+b)sinθ]〗^2 )
     
  2. jcsd
  3. Mar 20, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    Let vector a be along x-axis and vector b makes an angle theta with x-axis.
    Now take the component of b along x and y axis. Find net x component and y component and find the resultant.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof of Cosine law using vectors
  1. Cosine Law (Replies: 3)

  2. Proof using Gauss' Law (Replies: 5)

  3. Vector and cosine law? (Replies: 7)

Loading...