What is the 3-dimensional Euclidean plane?

Hi! the 3-dimensional euclidean plane is the standard plane we're taught from primary school. it is simply an X, Y, Z plane where coordinate points are in the form (x, y, z).

Hey there, you can think of a 2-dimensional Euclidian space as a flat piece of paper. If you want to describe a point on that paper it can done by showing how far the point is along each of the edges. For example : a point p could be said to be 2 cm along length and 5 cm along breadth. Similarly a 3 - dimensional Euclidean space will have 3 coordinates, for example, length, breadth, and height. So you’ll need 3 sets of measurements to describe a point in this space. Hope this helps.

It is simply the kind of space we live in, that represents a space with three dimensions: length, width, and height. It is defined by three mutually perpendicular axes commonly labeled as the x,y, and z axes. In this space, any point can be represented by a set of three coordinates (x,y,z), which specifies its position relative to the origin.

Imagine a map with x and y coordinates that would be 2 dimensional planes. If you then add a height coordinate above the map that would a z coordinate and thus create 3 dimensional Euclidean space.

The term "3-dimensional Euclidean plane" sounds a little confusing because it's a mixture of ideas. Let's break it down: 3-dimensional space: This is the space we live in. If you think about walking around, you can move left, right, forward, backward, and up and down. There are often three coordinates to represent this space: (x, y, z). We can write every point in space with just these three numbers. Euclidean: it is the geometry that any of us normally useit includes notions like points, lines, and shapeswhich behave just as we expect them to (like the angles in a triangle summing to 180 degrees). Plane: In geometry, a plane is the concept of a two-dimensional flat surface which extends in all directions endlessly. Imagine it like a piece of flat paper except without edges. So when your teacher said you were in the "3-dimensional Euclidean plane," they might have been referring to the full volume we live in—3-dimensional Euclidean space—or they might have been referring to a specific flat surface-a plane-within that space. Roughly speaking, what we know around us is 3D Euclidean space, and a plane is just an opened-up, flat surface inside that space. I hope it gave a clarity 😊.

3 Dimensions: x-axis (left and right), y-axis (forward and backward), z-axis (up and down). Coordinate System: Coordinate Framework: Coordinates, those are three numbers (x, y, z), are able to describe any place in space. For example, (3, 2, 5) indicates how far you may go in the x, y, and z directions to get to a given place. Imagine a room or a box. To describe any spot in the room, you can use three numbers: how far you are from one wall (x), from another wall (y), and how far off the floor (z). The Euclidean space is this 3D system.

The 3-dimensional Euclidean plane is just a fancy way of describing the space we live in using three directions: length (left and right), width (forward and backward), and height (up and down). It's called "Euclidean" because it follows the basic rules of geometry. In simple terms, it’s a way to pinpoint any location in 3D space by using three coordinates—one for each direction. For example, to find something in a room, you'd say how far it is from the walls (length and width) and how high it is off the ground (height)..

The 3-dimensional Euclidean plane (more accurately called 3-dimensional Euclidean space) is a mathematical model of the physical space we experience in everyday life. It is the generalization of the familiar 2-dimensional Euclidean plane to three dimensions. In this space, any point can be represented by three coordinates, corresponding to the three spatial dimensions.

Hey, the 3d Euclidean plane is the proper language for the standard planes of travel. That is X and Y (Could be imagined as left or right and up and down) and Z (Could be imagined as back and forth)