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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


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    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


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    The cross product of any vector with itself is 0. Not much point in doing that!
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