Vector Basics

A vector is a line in space with both direction and magnitude. Typically expressed as an arrow, a vector can show how an object moves relative to its position and velocity, otherwise known as momentum. 

The head of the vector is the end with the arrowhead, depicting which direction the object is heading, and the tail is the other end, showing where the object is.

There are a few methods to determine a vector's direction and magnitude mathematically.

To find the vector between two points, you would subtract one point from the other, creating the vector from the 2nd point to the first. For example, let's call the point at {0, 1} point 1. Then, let’s call the point at {2, 4} point 2. To find the vector with its tail at point 1 and its head at point 2, we would perform the following calculation: 

Point 1 = {0, 1}

Point 2 = {2, 4}

Point 2 - Point 1 = {2, 4} - {0, 1}

= {2 - 0, 4 - 1}

= {2, 3}

So, we have found that the vector connecting these two points would be {2, 3}. Here is a graphical depiction of the vector and the two points:

Vector Addition and Subtraction

In order to add two or more vectors together, you simply connect them tip-to-tail and create a vector spanning from the base of the two vectors to the end. This creates a vector that is equal to vector1 + vector2.

In this diagram, vector Z equals vector X + vector Y.

To subtract two vectors, you connect their tails and create a vector spanning from one tip to the other.