Question

the vector v has an initial point at (3, - 2) and a terminal point at (-1, - 8). plot the vector v and afterwards draw the directed line - segment. click and drag to draw the directed line - segment.

Explanation:

Step1: Recall vector - component formula

The components of a vector $\vec{v}$ with initial point $(x_1,y_1)$ and terminal point $(x_2,y_2)$ are given by $\vec{v}=\langle x_2 - x_1,y_2 - y_1
angle$. Here, $x_1 = 3,y_1=-2,x_2=-1,y_2 = - 8$.

Step2: Calculate the $x$ - component

$x_2 - x_1=-1 - 3=-4$.

Step3: Calculate the $y$ - component

$y_2 - y_1=-8-(-2)=-8 + 2=-6$.

Step4: Write the vector

The vector $\vec{v}=\langle - 4,-6
angle$.

To plot the vector:

1. First, plot the initial point $(3,-2)$ on the coordinate - plane.
2. Then, from the initial point, move 4 units to the left (because the $x$ - component is - 4) and 6 units down (because the $y$ - component is - 6) to reach the terminal point $(-1,-8)$. Draw an arrow from the initial point $(3,-2)$ to the terminal point $(-1,-8)$.

Answer:

The vector $\vec{v}=\langle - 4,-6
angle$ and it can be plotted with initial point $(3,-2)$ and terminal point $(-1,-8)$ as described above.