1. Not finding help here? Sign up for a free 30min 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!

Proving distributivity of Dot/Cross product

  1. Feb 5, 2012 #1
    Using the definitions in equations 1.1 and 1.4, and appropriate diagrams, show that the dot product and cross product are distributive;
    (a) when the three vectors are coplanar;
    (b) in the general case.

    Eq. 1.1) A dot B = ABcosθ

    Eq. 1.4) A cross B = ABsinθN

    This is exactly how my book puts the formulas.

    I know how the definition of the dot product is derived, and that it's distributive over vector addition, but I don't understand why they're asking why the three vectors are coplanar. I don't see where the third vector comes into play. I haven't even tried solving this on the cross product side because I know if I don't conceptually grasp the dot product part of it the cross product will only frustrate me.

    Here's my attempt at this proof:

    Part A: Stared at it for a while trying to figure it out and eventually gave up.

    Part B: Broke out the comfort food. Cried a little.

    1.2 Is the cross product associative?

    (Vector A cross Vector B) cross vector C (equals?) Vector A cross (Vector B cross Vector C)

    I know the cross product isn't associate because the order of the cross product determines the direction of the resultant vector, but I feel like there's more to it.

    Thank you all so much for your help!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 5, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The question is asking you to prove [itex] \vec{A}\cdot(\vec{B} + \vec{C}) = \vec{A}\cdot \vec{B} + \vec{A} \cdot \vec{C}, [/itex] and the same type of result using [itex] \times [/itex] instead of [itex] \cdot[/itex] . So, of course there have to be three vectors involved.

    RGV
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proving distributivity of Dot/Cross product
  1. Dot product (Replies: 5)

  2. Dot and cross product (Replies: 2)

  3. Dot and Cross Products (Replies: 3)

Loading...