∑ Mathematics Lab3D Space Geometry · v4.0.4

MATHEMATICS LAB · GEOMETRY

Analytic Geometry in 3D Space

Explore points, vectors, lines, and planes. Rotate the view, compare angles and distances, investigate intersections, and follow the step-by-step mathematics.

Coordinates are real numbers and angles are measured in degrees. Lines are infinite; the chart shows only a segment. The drawings are rotatable orthographic projections of three-dimensional objects.

1. Define objects in space

Three-dimensional coordinates and vectors
Point A
Point B
Point C

Vectors AB and AC start at A. Their lengths, dot product, and cross product determine the angle and area.

Examples:

2. Interactive 3D view

Orthographic projection · rotatable
Points and vectorsDrag to rotate the view; change the coordinates to update the constructions.
The 3D plot requires a browser supporting Canvas 2D. All results and calculations are available below the graph.

Drag the graph to rotate the view. Use the mouse wheel or the + and − buttons to zoom. Arrow keys rotate the view when the graph has focus. The XY, XZ, and YZ buttons show orthographic views. Edit the coordinates using the input fields above.

x-axis y-axis z-axis First object Second object Intersections Distances and perpendicular feet Angles

3. How to read the constructions

4. Results

Live updates

5. Explained calculations

Formulas, substitutions, interpretation

What you can study

Vectors in space

Magnitudes, point-to-point distances, dot and cross products, angles, and triangle areas.

Lines and planes

Parametric and Cartesian equations, intersections, parallelism, and skew lines.

Angles and distances

Line–plane and dihedral angle arcs, orthogonal projections, feet of perpendiculars, and minimum distances.

Lines and planes are infinite, while the graph displays finite portions. The app requires nonzero direction and normal vectors and uses numerical tolerances to identify coincidence and parallelism. The rotatable orthographic view does not change mathematical coordinates. Angle markers and perpendicular feet are 3D constructions that can be shown or hidden independently.