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Math Help - Algebraic Vectors

  1. #1
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    Algebraic Vectors

    1) The vector {\overrightarrow{v}} = [-6, -2] has tail A and head B. Graph each point A, and determine the coordinates of B.

    a) A(8, 5)

    How would I find the coordinates of B for the question? Do you find it by adding the x values together and the y values together?

    So. . .the coordinate of B for a) is. . .

    B(2, 3)?


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    2) Point A(5, -3) is the head of vector {\overrightarrow{v}}. Graph each vector {\overrightarrow{v}} and determine the coordinates of its tail.

    a) {\overrightarrow{v}} = [8, -5]

    Do I subtract the coordinate values with one another, so the tail of letter a is (3, -2)?
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  2. #2
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    Quote Originally Posted by Macleef View Post
    1) The vector {\overrightarrow{v}} = [-6, -2] has tail A and head B. Graph each point A, and determine the coordinates of B.

    a) A(8, 5)

    How would I find the coordinates of B for the question? Do you find it by adding the x values together and the y values together?

    So. . .the coordinate of B for a) is. . .

    B(2, 3)?
    With point A you have the stationary vector \overrightarrow{OA} too. You want to get the stationary vector \overrightarrow{OB} and you know that

    \overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA} = \vec v ~\implies~\overrightarrow{OB} = \vec v + \overrightarrow{OA}

    Your result is correct


    Quote Originally Posted by Macleef View Post
    2) Point A(5, -3) is the head of vector {\overrightarrow{v}}. Graph each vector {\overrightarrow{v}} and determine the coordinates of its tail.

    a) {\overrightarrow{v}} = [8, -5]

    Do I subtract the coordinate values with one another, so the tail of letter a is (3, -2)?
    According to the considerations above you have to subtract \vec v from \overrightarrow{OA} as you suggested. Unfortunately you made mistake:

    (5, -3) - (8, -5) = (-3, 2) That means you didn't calculate the vector \overrightarrow{OB} but \overrightarrow{BO}
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