Since the famous Descartes invented the plane rectangular coordinate system, the former ruler geometry has been transformed into analytic geometry, and geometric problems are described and proved by numbers, which is concise and efficient. Since then, mathematical research has entered a rapidly changing era. The development of spatial rectangular coordinate system is attributed to the power of the public. The Frenchman Fermat was the first to extend analytic geometry to three-dimensional space, and the Swiss johann bernoulli was the first to apply three-dimensional rectangular coordinate system. The word "coordinate" was invented by German Leibniz. But in the end it is called Cartesian space coordinate system, so it is very necessary to take the initiative.

There is also a right-handed spiral rule: the four fingers bend from the positive direction of the X axis to the positive direction of the Y axis, and then the thumb points to the positive direction of the Z axis. Or attach a picture to see.

Let a point coordinate in space be (,,), a point coordinate be (,), and the distance between two points be, then there is a formula:

It is expressed by the positive angle with the coordinate axis, and is defined as the angle with the X axis, the angle with the Y axis and the angle with the Z axis, and the range of angles [0, π]. There is a formula:

How to prove it? The process is as follows:

Let the distance between any point F in the space and the origin O be, and according to the formula of the distance between two points in the space, the result can be obtained by bringing in the above formula according to the definition of coordinates.