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!

Cross product of vectors

  1. Sep 27, 2013 #1
    i have a vector xK where k is the unit vector perpendicular to other unit vectors i and j
    when i multiply a force which has 5k for instance another which has ( 3 i + 4 j )
    i multiply 5k by 3i then 5k by 4j right ?
    the answer would be ( 15 j - 20 i ) right ?
     
  2. jcsd
  3. Sep 27, 2013 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    "5k for instance another which has ( 3 i + 4 j )
    i multiply 5k by 3i then 5k by 4j right ?"
    "the answer would be ( 15 j - 20 i ) right ? "
    If your k-vector is the left-hand factor in the cross product, yes.
    If your k-vector is your right-hand factor, the signs should be changed.
     
  4. Sep 28, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It's hard to make sense out of this. I presume you are asking specifically about the cross product of the vectors 5k and 3i+ 4j. The basic rules for the cross product is that ixj= k, jxk= i, kxi= j, the cross product is "anti- symmetric" (uxv= -vxu), and linear.

    The fact that the cross product is linear means that 5k x(3i+ 4j)= 15 kxi+ 20 kxj. The fact that the cross product is anti-symmetric means that kxj= -jxk= -i, so that 5k x (3i+ 4j)= 15j- 20i.

    Most people remember the cross product with the mnemonic
    [tex](ai+ bj+ ck)\times (di+ ej+ fk)= \left|\begin{array}{ccc}i & j & k \\ a & b & c \\ d & j & k\end{array}\right|[/tex]
    where the right side is the determinant.

    Here, that would give
    [tex]5k \times 3i+ 4j= \left|\begin{array}{ccc}i & j & k \\ 0 & 0 & 5 \\ 3 & 4 & 0 \end{array}\right|[/tex]
    Expanding the determinant on the second row, that is
    [tex]-5\left|\begin{array}{cc}i & j \\ 3 & 4 \end{array}\right|= -5(4i- 3j)= 15j- 20i[/tex]
     
    Last edited: Sep 28, 2013
  5. Sep 28, 2013 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The determinant looks wrong.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Cross product of vectors
Loading...