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!

Homework Help: Solving 2 vectors with cross product

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Two vectors are given by A = -6 i + 5 j and B = 1 i + 4 j
    Find A X B (answer only in terms of i, j, k)
    Find the angle between A and B (answer is terms of degrees)

    2. Relevant equations
    All I was told was that if I set a 3x3 matrix like this:
    i j k
    -6 5 0
    1 4 0
    then AxB is the determinant

    3. The attempt at a solution
    I made the 3x3 matrix and found the determinant to be only -29 k, which I am told is correct.
    I have absolutely no idea on how to approach the angle problem. If I may ask, can someone get me started in the right direction for that problem?
  2. jcsd
  3. Nov 22, 2012 #2


    User Avatar
    Homework Helper

    Look up the definition of cross product (here).

    You will see that you can calculate AxB in terms of a unit vector.
  4. Nov 22, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Have you had the formula ##\vec a \cdot \vec b = |\vec a||\vec b|\cos\theta##? That might come in handy.
  5. Nov 22, 2012 #4
    ##|\vec a \times \vec b| = |\vec a||\vec b|\sin\theta##
  6. Nov 23, 2012 #5
    Why thanks, you two! I vaguely remember the dot product equation from precalculus (all those years ago), but the cross product one I've never seen. Thanks!
  7. Nov 23, 2012 #6


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You're welcome. I might add that since the angle between two vectors is always between 0 and ##\pi##, the dot product may be slightly more convenient because that is the principle range of the inverse cosine.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook