Relationship Between Vector Coordinates and the Coordinates of its Start and End Points
🎯 Core Concept
A vector is a mathematical object that has both magnitude (length) and direction. When we place a vector in a coordinate plane, we can describe it using the coordinates of its start point (initial point) and end point (terminal point).
📐 The Fundamental Formula
If a vector $\vec{AB}$ has:
- Start point (initial point): $A(x_1, y_1)$
- End point (terminal point): $B(x_2, y_2)$
Then the coordinates of the vector $\vec{AB}$ are:
$$\vec{AB} = (x_2 - x_1,\; y_2 - y_1)$$
In words: To find the vector coordinates, subtract the start point coordinates from the end point coordinates. It's always "end minus start".