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Thread: Algebraic Vectors

  1. #1
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    Algebraic Vectors

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

    a) $\displaystyle A(8, 5)$

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

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

    $\displaystyle B(2, 3)$?


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

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

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

    a) $\displaystyle A(8, 5)$

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

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

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

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

    Your result is correct


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

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

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

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