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Math Help - Simple vector question

  1. #1
    Super Member 11rdc11's Avatar
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    Simple vector question

    Ok for some reason I'm not understanding this question or how to approach it

    Express i and j in terms of a and b

    a = 2i + 3j
    b = i-j

    Any help would be great, thanks.


    The answer is

    i =\frac{1}{5}a +\frac{3}{5}b

    j = \frac{1}{5}a -\frac{2}{5}b
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by 11rdc11 View Post
    Ok for some reason I'm not understanding this question or how to approach it

    Express i and j in terms of a and b

    a = 2i + 3j
    b = i-j

    Any help would be great, thanks.


    The answer is

    i =\frac{1}{5}a +\frac{3}{5}b

    j = \frac{1}{5}a -\frac{2}{5}b
    Note that (first eq) + 3*(second eq) will eliminate the j terms. This gives us a+3b=5i. Solving for i, we get \frac{a}{5}+\frac{3b}{5}.

    Now substitute this into either equation to solve for j.

    Can you take it from here?
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  3. #3
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    Just treat the vectors as a system of equations.
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  4. #4
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Note that (first eq) + 3*(second eq) will eliminate the j terms. This gives us a+3b=5i. Solving for i, we get \frac{a}{5}+\frac{3b}{5}.

    Now substitute this into either equation to solve for j.

    Can you take it from here?
    Wow I was completly overthinking that lol. Thanks again
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