To determine the vector that goes from point [tex]\( (4,0) \)[/tex] to point [tex]\( (1,-3) \)[/tex], we need to follow a detailed, step-by-step solution.
1. Identify the Coordinates of the Points:
- Let point [tex]\( A \)[/tex] be [tex]\( (4,0) \)[/tex].
- Let point [tex]\( B \)[/tex] be [tex]\( (1,-3) \)[/tex].
2. Determine the Components of the Vector:
- The vector going from [tex]\( A \)[/tex] to [tex]\( B \)[/tex] can be found by subtracting the coordinates of point [tex]\( A \)[/tex] from point [tex]\( B \)[/tex].
3. Subtract the x-coordinates:
- The x-component of the vector is calculated as:
[tex]\[
B_x - A_x = 1 - 4 = -3
\][/tex]
4. Subtract the y-coordinates:
- The y-component of the vector is calculated as:
[tex]\[
B_y - A_y = -3 - 0 = -3
\][/tex]
5. Combine the components into a vector:
- Therefore, the vector that goes from [tex]\( (4,0) \)[/tex] to [tex]\( (1,-3) \)[/tex] is:
[tex]\[
\vec{v} = (-3, -3)
\][/tex]
Hence, the vector that goes from [tex]\( (4,0) \)[/tex] to [tex]\( (1,-3) \)[/tex] is [tex]\((-3, -3)\)[/tex]. This is the correct resultant vector.
