Everything in the real world is in a three-dimensional shape. You can simply look around and observe! Even a flat piece of paper has some thickness if you look sideways. A strand of your hair or a big-sized bus, all of them have a three dimensional geometry. And it is necessary to learn their properties. So, let’s start by understanding lines, planes, and angles from the topics below.
- Angle Between a Line and a Plane
- Angle Between Two Lines
- Coplanarity of Two Lines
- Angle Between Two Planes
- Direction Cosines and Direction Ratios of a Line
- Distance Between Parallel Lines
- The Distance Between Two Skew Lines
- Distance of a Point from a Plane
- Equation of a Plane in Normal Form
- Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point
- The Equation of Line for Space
- Equation of Plane Passing Through Three Non Collinear Points
- Intercept Form of the Equation of a Plane
- Plane Passing Through the Intersection of Two Given Planes
FAQs on Three Dimensional Geometry
Question 1: What is meant by 3d geometry?
Answer: 3D geometry refers to the mathematics of shapes in three-dimensional space and consists of 3 coordinates. These 3 coordinates are x-coordinate, y-coordinate and z-coordinate. In three-dimensional space, there is a requirement of three parameters for the purpose of finding the exact location of a point.
Question 2: What is meant by the word dimension in the field of geometry?
Answer: Dimension, in common parlance, denotes the measure of an object’s size, such as a box, usually given as height, length, and width. In geometry, the notion of dimension is an extension of the idea that a line represents one-dimensional, a plane happens to be two-dimensional, and space is three-dimensional.
Question 3: Explain how do 3d coordinates work?
Answer: The formation of a three-dimensional Cartesian coordinate system is by a point known as the origin as well as a basis involving three mutually perpendicular vectors. These vectors properly explain the three coordinate axes which are: the x−, y−, and z−axis. Experts also call them as abscissa, ordinate and applicate axis, respectively.
Question 4: Can we say our world is three-dimensional?
Answer: Yes, our world is certainly three-dimensional because our universe is three-dimensional.