To determine the components of the vector [tex]\( v \)[/tex] given its initial and terminal points, we follow these steps:
1. Identify the coordinates of the initial point and the terminal point.
The initial point of the vector [tex]\( v \)[/tex] is [tex]\((-1, -3)\)[/tex].
The terminal point of the vector [tex]\( v \)[/tex] is [tex]\((-7, -7)\)[/tex].
2. Calculate the x-component of the vector [tex]\( v \)[/tex].
The x-component can be found by subtracting the x-coordinate of the initial point from the x-coordinate of the terminal point:
[tex]\[
v_x = -7 - (-1) = -7 + 1 = -6
\][/tex]
3. Calculate the y-component of the vector [tex]\( v \)[/tex].
The y-component can be calculated by subtracting the y-coordinate of the initial point from the y-coordinate of the terminal point:
[tex]\[
v_y = -7 - (-3) = -7 + 3 = -4
\][/tex]
4. Combine the x-component and y-component to form the component form of the vector [tex]\( v \)[/tex].
Therefore, the components of the vector [tex]\( v \)[/tex] are [tex]\((-6, -4)\)[/tex].
Answer: [tex]\((-6, -4)\)[/tex]
