1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Question about property of Cross Product

  1. Dec 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Hello. I am relatively new to this subject please forgive my incompetence.
    Please correct me if I have misunderstandings.

    I understand that the cross product of two vectors (say A and B) in R3 is a vector that is orthogonal to both A and B. But how A x B be orthogonal to the plane spanned by A and B?

    I don't understand what this plane spanned by A and B should look like geometrically.

    Wouldn't A x B be parallel to the plane spanned by A and B?
  2. jcsd
  3. Dec 5, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Think of your two vectors A and B positioned with their tails together and assume they are not parallel. Think of the parallelogram created using those vectors as two sides of the parallelogram. That parallelogram is part of the plane spanned by A and B. A x B is perpendicular to that plane.
  4. Dec 5, 2009 #3
    Oh okay I got that mixed up then. Thanks.

    So then the plane by spanning A and B has the vectors A and B as the boundaries right?
    Why does it make a parallelogram when there is only two vectors?

    Now my next question is how to understand the weird order in which you multiply the elements of A and B to get A x B?

    The vector gotten from A x B is only from the point where A and B intersect?
  5. Dec 5, 2009 #4


    User Avatar
    Homework Helper

    A plane has no boundaries. The vectors are two sides of the parallelogram, and the other two sides can be drawn parallel to the original two vectors to complete the parallelogram.

    Wikipedia has some nice pictures which may help clarify things:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Question property Cross Date
Set notation question Mar 8, 2018
Question of the basic properties of tan Sep 19, 2013
Quadratic Properties Question Apr 4, 2012
Question about simple algebraic exponential property Jul 27, 2009
Properties of logs question Dec 3, 2008