Kinematics in Two and Three Dimensions

Vector Addition and Subtraction

First, we need to understand how to calculate vector direction and magnitude.

Here is the equation to calculate direction (or angle) of the resultant vector.

Here is the equation for the magnitude of the resultant.

Lets look at vector addition.

Now let's look at vector subtraction.

So, in vector addition, add the x component of the first vector to the x component of the second one to get the x component of the resultant. Same principle applies to the y component. And, in vector subtraction, subtract the x component of the second vector from the x component of the first vector to get the x component of the resultant. Same principle applies to the y component. Then, you can get direction from the angle formula.

© April, 1998, Montana State University-Bozeman