Find the components of the vector 𝐴𝐵, where 𝐴 is the point with coordinates five, two and 𝐵 is the point with coordinates 17, 23.
So we’ve been given the initial and terminal points of a vector and asked to find its components. To do this, we need to record that if a vector has an initial point with coordinates 𝑥 one, 𝑦 one and a terminal point with coordinates 𝑥 two, 𝑦 two, then the components of the vector can be found by subtracting the coordinates of the initial point from the terminal point.
The components of the vector are 𝑥 two minus 𝑥 one, 𝑦 two minus 𝑦 one. So let’s apply this to the vector 𝐴𝐵. The first component of the vector 𝐴𝐵, the horizontal component, is 17 minus five.
The second component the vertical part is 23 minus two. Therefore, in component form, the vector 𝐴𝐵 is 12, 21.