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Vector Question - u = u1+u2 where u1 is parallel

  1. Jun 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Let u = i - 2j, v = 2i + 3j, and w = i + j. Write u = u1 + u2 where u1 is parallel to v and u2 is parallel to w. (See question 41.)


    2. Relevant equations

    Properties of vectors. Question 41: https://answers.yahoo.com/question/index?qid=20090923151849AARqpWR

    3. The attempt at a solution

    I haven't had much of an attempt at this because I don't how to determine analytically if a vector is parallel to another vector. Through google I found that a vector A is parallel to a vector B if their dot product, A dot B, equals 0. But this question comes immediately before the Dot Product section of my calculus textbook, so I'm assuming there's a way to figure it out using other methods.

    I'd appreciate any advice pointing me towards the right v/|v|.... (get it?)

    Thanks
     
  2. jcsd
  3. Jun 25, 2014 #2

    LCKurtz

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    The easy test for parallel is one vector is a multiple of the other.

    No, that is the test for two vectors to be perpendicular.

     
  4. Jun 25, 2014 #3
    You're correct. I meant to say that if the cross product equals 0, then they are parallel. http://mathworld.wolfram.com/ParallelVectors.html


    But onto what you said. So a vector A is parallel to a vector B if, say, A = i + j and B = 2i + 2j?

    Thanks
     
  5. Jun 26, 2014 #4

    ehild

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    Yes, a vector A is parallel with vector B if B=kA , with k a scalar.

    ehild
     
  6. Jun 26, 2014 #5

    HallsofIvy

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    Basically this problem asks you to find numbers, a and b, such that u= av+ bw. That is, such that
    1- 2j= a(2i+ 3j)+ b(i+ j). You have to solve two equations in two unknowns.
     
  7. Jul 1, 2014 #6
    Much to my chagrin I haven't had any luck with this problem. Would someone be able to give a brief work through or perhaps continue leading me in the right direction? It's probably so easy that a small hint would almost give the problem away...

    Thanks
     
  8. Jul 1, 2014 #7

    LCKurtz

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    Show us what happened when you tried HallsOfIvy's suggestion in post #5.
     
    Last edited: Jul 2, 2014
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