Question Video: Using Initial and Terminal Points to Find the Components of a Vector Mathematics • First Year of Secondary School

Video Transcript

Consider the vector 𝐀𝐁 for point 𝐴 with coordinates three, two and 𝐵 with coordinates six, nine. Write vector 𝐀𝐁 in component form 𝑎, 𝑏.

To find the components 𝑎 and 𝑏 of the vector 𝐀𝐁, we consider the horizontal and vertical distances and directions from 𝐴, which is the initial point, to 𝐵, which is the terminal point. We see that the horizontal distance is three units moving to the right. So 𝑎 is positive three. And in fact this is the difference between the two 𝑥-coordinates of points 𝑎 and 𝑏, that is, six minus three, which is positive three. The vertical distance is seven units up. That’s positive seven. And this is the difference between the 𝑦-coordinates of the two points 𝐴 and 𝐵. Hence, we can write the vector from 𝐴 to 𝐵 as 𝐀𝐁 equals three, seven.