How do you rotate a vector 90 degrees?

Rotating Vectors 90 Degrees: A Human’s Guide

Vectors. We encounter them everywhere, from physics class to video games, but have you ever stopped to think about how to actually rotate one? It’s a surprisingly useful trick, and once you get the hang of it, you’ll find all sorts of applications for it. So, let’s dive in and explore how to rotate a vector by 90 degrees, both clockwise and counterclockwise.

At its heart, rotating a vector simply means changing its direction while keeping its length the same. Think of it like spinning an arrow around a central point. Now, in the familiar world of x and y axes, we usually represent a vector as a pair of numbers, (x, y). These numbers tell us how far the vector stretches along each axis.

One of the slickest ways to handle vector rotation is with something called a rotation matrix. A rotation matrix is basically a special tool that, when multiplied by your vector, magically spins it around the origin.

For a 90-degree spin in the counterclockwise direction, our magic matrix looks like this: