How do you find out the unit vector of given two points?

Answer 1

Prescript: I was going to ask why you'd ask this in Humor, but the fact that I even answered this seriously is funny enough.

TL;DR - Subtract Point Vector A from Point Vector B, divide the squares of the x and y values of remaining vector by (x^2 + y^2)

Thought Process

If I remember my linear mathematics correctly, a unit vector is standard coordinate vector with a length of 1, right? So you just want to convert your normal vector (point B - point A values) to a vector of length one.

Take a vector from point (1 1) to point (4 5).

Standard vector is (3 4) from origin (1 1). The length of this is 5, obviously.

We found that using 3^2 + 4^2 = 5^2, right? To get that length to 1, we have to divide through by 5^2.

(3^2/5^2) + (4^2/5^2) = 1

:. 9/25 + 16/25 = 1 Yep. So for this particular point-to-point, the unit vector is (9/25 16/25)

So we know now that A^2/length^2 + B^2/length^2 = 1. Those A and B bits make up the vector. We also know that A^2 + B^2 = length^2.

So we can make a general formula for this, one you can always use when you have to do this once you've created a single vector:

A^2/(A^2 + B^2) + B^2/(A^2 + B^2) = 1

Hooray.