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Thread: Algebraic Vectors

  1. #1
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    Algebraic Vectors

    Let vector $\displaystyle m = [2, -1]$ and vector $\displaystyle b = [0, 5]$

    a) Determine the components of each vector in this list:

    $\displaystyle b + 3m = [6, 2]$

    $\displaystyle b + 2m = [4, 3]$

    $\displaystyle b + m = [2, 4]$

    $\displaystyle b + 0m = [0, 5]$

    $\displaystyle b - m = [-2, 6]$

    $\displaystyle b - 2m = [-4, 7]$

    $\displaystyle b - 3m = [-6, 8]$

    b) Graph all 7 vectors in part a with tail at $\displaystyle [0, 0]$



    c) Explain the pattern in the results. ------- Does this mean the graph increases or decreases 2 units for the x values and the y values goes increases or decreases 1 unit? ----------- If I'm correct, is there a correct term to use for it?

    d) How would the above results be affected if vector b were replaced with each vector? ------ I don't see a pattern for the next two. . .Do I use a specific formula to find the pattern?

    i) $\displaystyle b = [2,4]$

    $\displaystyle b + 3m = [8, 11]$

    $\displaystyle b + 2m = [8, 7]$

    $\displaystyle b + m = [4, 3]$

    $\displaystyle b + 0m = [2, -1]$

    $\displaystyle b - m = [0, -5]$

    $\displaystyle b - 2m = [-2, -9]$

    $\displaystyle b - 3m = [-4, -13]$


    ii) $\displaystyle b = [-1, 2]$

    $\displaystyle b + 3m = [-1, 5]$

    $\displaystyle b + 2m = [0, 3]$

    $\displaystyle b + m = [1, 1]$

    $\displaystyle b + 0m = [2, -1]$

    $\displaystyle b - m = [3, -3]$

    $\displaystyle b - 2m = [4, -5]$

    $\displaystyle b - 3m = [5, -7]$
    Last edited by Macleef; Feb 14th 2008 at 11:29 AM.
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  2. #2
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    Quote Originally Posted by Macleef View Post
    Let vector $\displaystyle m = [2, -1]$ and vector $\displaystyle b = [0, 6]$

    a) Determine the components of each vector in this list:
    $\displaystyle b + 3m = [6, 2]$
    $\displaystyle b + 2m = [4, 3]$
    $\displaystyle b + m = [2, 4]$
    $\displaystyle b + 0m = [0, 5]$ ... I don't understand how you get these results
    $\displaystyle b - m = [-2, 6]$
    $\displaystyle b - 2m = [-4, 7]$
    $\displaystyle b - 3m = [-6, 8]$
    b) Graph all 7 vectors in part a with tail at $\displaystyle [0, 0]$



    ...
    Your calculations of the coordinates of the heads of the vectors are wrong.

    For instance: $\displaystyle b + 2m = (0, 6) + 2 \cdot (2, -1) = (0, 6) + (4, -2) = (4, 4)$

    The heads of all vectors form the line $\displaystyle y = -\frac12 x + 6$ or written as equation with vectors:

    $\displaystyle (x, y) = (0, 6) + r \cdot (2, -1)$
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  3. #3
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    It's a typo in my part, it's b[0, 5] and not b[0, 6]
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  4. #4
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    Quote Originally Posted by Macleef View Post
    It's a typo in my part, it's b[0, 5] and not b[0, 6]
    Then your results are OK.

    The heads of all vectors form the line $\displaystyle y = -\frac12 x + 5$ or written as equation with vectors:

    $\displaystyle (x, y) = (0, 5) + r \cdot (2, -1)$
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