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How can I solve this proof?

  1. Oct 14, 2010 #1
    1. The problem statement, all variables and given/known data
    The following are all vectors:
    a, b, c, d

    k = (a+b) (c+d)

    prove: k = (a x c) + (a x d) + (b x c) + (b x d)

    2. Relevant equations

    3. The attempt at a solution
    I have tried to start it by doing:

    |a| = a = sqrt(a_x^2 + a_y^2)

    is that a correct start at it? I really am pretty lost...
  2. jcsd
  3. Oct 14, 2010 #2
    As per my other post, do you understand how to expand the brackets to get between the two solutions for k?

  4. Oct 14, 2010 #3
    I guess I don't...Could you please explain?
  5. Oct 14, 2010 #4
    Have a read through this:

    http://richardbowles.tripod.com/maths/algebra/brackets.htm [Broken]

    It will show you how to expand the brackets.
    Last edited by a moderator: May 5, 2017
  6. Oct 14, 2010 #5
    Oh, yeah I know how to do that but what if what I meant by "k = (a+b) (c+d)" was actually the dot product of k = (a+b) (c+d) instead of just k = (a+b) x (c+d)? Does that make a difference?
  7. Oct 14, 2010 #6
    k = (a+b)(c+d) = (a+b)x(c+d) = (a x c)+(a x d)+(b x c)+(b x d)

    What you have there is expanding the brackets, this is not the dot product.

    The dot product of [a,b][c,d] = ac + bd.

    The question shows bracket expansion not dot product. So yes, there is a difference, particularly in notation (dot product = square brackets with commas seperating vectors, expansion = round brackets with standard mathematical operators).
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