Class 11 Maths - BIHAR
Introduction to Three Dimensional Geometry
The Chapter 'Introduction to Three Dimensional Geometry' in Class 11 Mathematics builds upon your knowledge of 2D coordinate geometry by adding a third dimension, the z-axis. You will learn how to locate points in space using ordered triplets (x, y, z), understand the concept of octants, and calculate distances between two points in a 3D Cartesian coordinate system. This chapter is vital as it forms the foundational base for vector algebra and calculus in 3D, which are heavily tested in BSEB board examinations and competitive entrance tests like JEE.
Start Learning FreeKey Concepts
Three-Dimensional Cartesian Coordinate System
Space is defined by three mutually perpendicular axes called the x-axis, y-axis, and z-axis, intersecting at a point called the origin (0, 0, 0).
Octants
The three coordinate planes divide the space into eight parts known as octants, similar to how four quadrants divide a 2D plane.
Coordinates of a Point in Space
Every point in 3D space is represented by an ordered triplet (x, y, z) which gives its perpendicular distances from the yz, xz, and xy planes respectively.
Distance Formula in 3D
The straight-line distance between any two points P(x1, y1, z1) and Q(x2, y2, z2) in space is found using an extension of the Pythagorean theorem.
Section Formula
Used to find the coordinates of a point that divides the line segment joining two given points in a specific ratio, both internally and externally.
Important Formulas
Board Exam Info
In the Bihar School Examination Board (BSEB) Class 11 Mathematics examination, Coordinate Geometry (including 3D geometry) generally carries around 8 to 12 marks. Questions frequently include 1-mark objective (MCQs), 2-mark short answer questions based on the distance formula, and occasional long-answer questions utilizing the section or midpoint formulas.
Frequently Asked Questions
How do I determine the sign of coordinates in different octants?
Just like quadrants in 2D, octants depend on the positive and negative directions of the x, y, and z axes. For example, in the first octant (XOYZ), all coordinates (x, y, z) are positive (+, +, +).
Is 3D geometry very different from 2D coordinate geometry?
Not really! Most formulas like the distance formula, section formula, and midpoint formula are just extended by adding a z-component to them.
What is the coordinate of a point on the x-axis in 3D space?
Any point lying on the x-axis has y and z coordinates as zero, so it is represented as (x, 0, 0).
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