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Finding Two Vectors from Vector Sum / Difference

  1. Sep 3, 2013 #1

    Cod

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    Finding Two Vectors from Given Linear Combination

    1. The problem statement, all variables and given/known data
    If v + w = (5,1) and v - w = (1,5), compute and draw v and w.

    2. Relevant equations
    v + w = (5,1)
    v - w = (1,5)

    3. The attempt at a solution
    I understand how to find the sum of two vectors, but I'm confused on how to find the vectors from a sum / difference. My first attempt was to draw the v + w vector and v - w vector and try to visualize the original two vectors, v and w. However, I couldn't come up with anything productive.


    If it matters, I'm going through MIT OCW 18.06 w/ Introduction to Linear Algebra (Strang) and this is question 3 from problem set 1.1. Its been a few years since I took LA or any vector math and I'm trying to regain lost knowledge.

    Any guidance would be greatly appreciated.
     
    Last edited: Sep 3, 2013
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  3. Sep 3, 2013 #2

    SteamKing

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    Staff Emeritus
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    Homework Helper

    "I understand how to find the sum of two vectors, but I'm confused on how to find the vectors from a sum / difference."

    What happens if you add the two equations together in Section 2 of the OP? What happens if you subtract them?
     
  4. Sep 3, 2013 #3

    Cod

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    Adding them would give 2v = (6,6), which would make vector v = (3,3). Subtracting them would give 2w = (4,-4), which would make vector w = (2,-2).

    Wow, wish I would've seen that on my own. Thanks for the "nudge" in the correct direction.
     
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