# Math Help - Algebraic Vectors

1. ## 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 $(3, -2)$?

2. Originally Posted by Macleef
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

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

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 $\overrightarrow{BO}$