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.
