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Let the vector [tex]$\mathbf{v}$[/tex] have an initial point at [tex][tex]$(-1,-3)$[/tex][/tex] and a terminal point at [tex]$(-7,-7)$[/tex]. Determine the components of vector [tex]$\mathbf{v}$[/tex].

Answer: [tex]$\square$[/tex]
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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]
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