3D Geometry

The moving power of mathematical invention is not reasoning but imagination. – A.DEMORGAN

We constantly describe both the shapes and positions of three dimensional objects. For example, one simple way to describe a 3D object is to approximate its shape as a mesh of triangles. Each triangle is de?ned by three vertices, and the positions of each of these vertices will have to be described by three coordinates [x,y,z]t.

In this chapter, we shall study the direction cosines and direction ratios of a line joining two points and also discuss about the equations of lines and planes in space under different conditions, angle between two lines, a line and a plane, shortest distance between two skew lines and distance of a point from a plane.

Lower level geometry of planes and graphical two dimensional coordinates moves into a three dimensional space in three dimensional geometry.

Topics Covered: 

• Rectangular Co-ordinate System in Space
• Direction Cosines of Line
• Direction Ratios
• Parallel Lines
• Projection of Line
• Theory of 3D Plane
• Theory of 3D Straight Line
• Shortest Distance-two Non Intersecting Lines
• Theory of Sphere
• Solved Problems of 3D Geometry Part I
• Solved Problems of 3D Geometry Part II
• Solved Problems of 3D Geometry Part III
• Solved Problems of 3D Geometry Part IV
• Solved Problems of 3D Geometry Part V
• Solved Problems of 3D Geometry Part VI