Cheexorgeny

2022-01-04

Find a vector a with representation given by the directed line segment AB. Draw AB and the equivalent representation starting at the origin.
$A\left(-2,I\right)$, $B\left(l,2\right)$

Laura Worden

Given $A\left(-1,1\right)$, $B\left(3,2\right)$
Substract the corresponding components of A and B
$a=\stackrel{\to }{AB}=<3-\left(-1\right),2-1\ge <4,1>$
The equivalent representation is a vector from the point $\left(0,0\right)$ to $\left(4,1\right)$

user_27qwe

To find the vector $\stackrel{\to }{a}$ with the representation given by the directed line segment $AB$, where $A\left(-2,1\right)$ and $B\left(1,2\right)$, we can use the formula:
$\stackrel{\to }{a}=\stackrel{\to }{B}-\stackrel{\to }{A}$
Substituting the values of $A$ and $B$, we have:
$\stackrel{\to }{a}=\left[\begin{array}{c}1\\ 2\end{array}\right]-\left[\begin{array}{c}-2\\ 1\end{array}\right]$
Simplifying the subtraction, we get:
$\stackrel{\to }{a}=\left[\begin{array}{c}1-\left(-2\right)\\ 2-1\end{array}\right]$
Thus, the vector $\stackrel{\to }{a}$ is:
$\stackrel{\to }{a}=\left[\begin{array}{c}3\\ 1\end{array}\right]$
Now, let's draw the line segment $AB$ and the equivalent representation of $\stackrel{\to }{a}$ starting at the origin.
[Drawing]
As shown in the drawing, the line segment $AB$ extends from the point $A\left(-2,1\right)$ to the point $B\left(1,2\right)$. The vector $\stackrel{\to }{a}$ with representation starting at the origin is represented by the arrow starting at the origin and ending at the point $\left(3,1\right)$.

karton

Step 1:
The vector representation of a line segment from point A to point B is given by the difference between the coordinates of B and A. Therefore, the vector $𝐚$ can be found as:
$𝐚=𝐁-𝐀$
Given that point A is $A\left(-2,1\right)$ and point B is $B\left(1,2\right)$, we can calculate the vector $𝐚$ as:
$𝐚=\left(\begin{array}{c}1\\ 2\end{array}\right)-\left(\begin{array}{c}-2\\ 1\end{array}\right)$
Simplifying this expression, we get:
$𝐚=\left(\begin{array}{c}1+2\\ 2-1\end{array}\right)$
$𝐚=\left(\begin{array}{c}3\\ 1\end{array}\right)$
Step 2:
Now, let's draw the directed line segment AB and the vector representation starting from the origin.
$AB$:
To draw $AB$, we start at point A $\left(-2,1\right)$ and end at point B $\left(1,2\right)$.
$\stackrel{\to }{AB}$:
To draw the vector representation $\stackrel{\to }{AB}$ starting from the origin, we start at the origin $\left(0,0\right)$ and end at the coordinates of B $\left(1,2\right)$.
Now, let's visualize this on a coordinate plane:
$AB$:
- Draw a line segment from point A $\left(-2,1\right)$ to point B $\left(1,2\right)$.
$\stackrel{\to }{AB}$:
- Draw an arrow starting from the origin $\left(0,0\right)$ and ending at the coordinates of B $\left(1,2\right)$.
By following these steps, you should be able to solve the problem and draw the directed line segment AB and its equivalent vector representation starting from the origin.

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