Three dimensional geometry

 Three-dimensional geometry deals with objects and spaces in three dimensions. Some key concepts include:

  1. Coordinates: In a three-dimensional space, you use three coordinates (x, y, and z) to pinpoint a location.


  3. Vectors: Vectors are commonly used to represent direction and magnitude in 3D space. They can be added, subtracted, and multiplied by scalars.


  5. Distance and Length: You can calculate the distance between two points in 3D space using the 3D distance formula, which is an extension of the Pythagorean theorem.


  7. Lines and Planes: Understanding equations for lines and planes in 3D space is essential. Lines are represented by parametric equations, while planes have normal vectors and point representations.


  9. Dot and Cross Products: These operations are used extensively in 3D geometry. The dot product gives the projection of one vector onto another, while the cross product yields a vector perpendicular to both input vectors.


  11. Vectors and Parametric Equations of Curves: Curves like lines, circles, and ellipses can be represented using parametric equations involving vectors.


  13. Solid Geometry: This involves the study of 3D shapes like spheres, cylinders, cones, and polyhedra. You can calculate their volume, surface area, and other properties.


  15. Transformation in 3D: Transformations like translation, rotation, and scaling are important in 3D geometry and computer graphics.


  17. Coordinate Systems: Cartesian coordinates are common, but there are other systems like spherical and cylindrical coordinates that are useful for certain problems.

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