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

When to us dot versus cross product

  1. Nov 8, 2008 #1
    Hi folks,
    When you're squaring the sum of two vectors (v_1 + v_2)^2, why is it that it comes out as v_1 dot v_1 plus 2*v_1 dot v_2 plus v_2 dot v_2? Why do we use the dot product here instead of cross product? I understand that dot product is the multiplication of their parallel components, but it seems arbitrary to use dot rather than cross product in this case
  2. jcsd
  3. Nov 8, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    dot products: v.w = |v| |w| cos(t), hence these are used to measure lengths and angles.

    well i guess it isn't so clear from this description, but cross products are used to measure areas, i.e. |vxw| = |v||w| sin(t).

    the reason is that one gives the length of the projection of v onto w, and the other gives the length of the projection of v perpendicular to w, hence gives the height needed to compute area of the parallelogram they span.
  4. Nov 8, 2008 #3


    User Avatar
    Science Advisor

    The cross product of any vector with itself is 0. Not much point in doing that!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - versus cross product Date
I Motivation and proof behind cross products Oct 15, 2016
Adjoint versus classical adjoint/any relation? May 30, 2011
Bijective versus Linear Sep 26, 2010
AX=B versus Ax=b Jan 7, 2009
Givens rotations versus Euler angles Aug 26, 2008