Plücker coordinates

Imagine you have a toy car. You can describe its position using two numbers- the x position and y position. But what if you want to describe the car's position and direction it is facing?

This is where Plücker coordinates come in. Plücker coordinates are a way to describe the position and direction of a line in 3-dimensional space.

Just like how we needed two numbers to describe the position of the toy car, we need six numbers to describe the position and direction of a line. These numbers are called the Plücker coordinates.

The first three Plücker coordinates describe the position of the line. They are the x, y, and z coordinates of any point on the line.

The next three Plücker coordinates describe the direction the line is pointing. They are a set of three numbers that represent the direction of the line relative to the x, y, and z axes.

Using these six numbers, we can perfectly describe the position and direction of any line in 3D space.

So, just like how we use two numbers to describe the position of a toy car and six numbers to describe the position and direction of a line in 3D space, Plücker coordinates help us describe lines in 3D space using six numbers.