Class 11 Maths - CBSE
Introduction to Three Dimensional Geometry
The Introduction to Three Dimensional Geometry chapter in Class 11 CBSE Mathematics builds upon your previous knowledge of 2D coordinate geometry by introducing the third dimension, the z-axis. You will learn how to locate points in space using ordered triplets (x, y, z), divide space into eight octants, and calculate distances between points. This chapter forms a crucial foundation for vectors and 3D geometry in Class 12, making it essential for scoring well in your CBSE board examinations and engineering entrance tests.
Start Learning FreeKey Concepts
Coordinate Axes and Planes
Space is defined by three mutually perpendicular axes called the x-axis, y-axis, and z-axis, which intersect at the origin and divide space into three coordinate planes: XY, YZ, and ZX.
Octants
The three coordinate planes divide the three-dimensional space into eight parts known as octants, similar to how quadrants divide a 2D plane.
Coordinates of a Point in Space
Any point P in space is represented by an ordered triplet (x, y, z), representing its perpendicular distances from the YZ, ZX, and XY planes respectively.
Distance Formula
The straight-line distance between any two points P(x1, y1, z1) and Q(x2, y2, z2) in 3D space is calculated using an extension of the Pythagorean theorem.
Section Formula
Coordinates of a point that divides the line segment joining two points internally or externally in a given ratio m:n in 3D space.
Important Formulas
Board Exam Info
In the CBSE Class 11 Mathematics examination, this chapter along with Limits and Derivatives usually contributes around 4 to 6 marks. Common question types include finding the coordinates of a point using geometric conditions, finding the ratio in which a line segment is divided, proving geometric shapes (like vertices of a triangle or parallelogram), and applying the distance formula.
Frequently Asked Questions
How do I determine the sign of coordinates in different octants?
Just like the four quadrants in 2D, the eight octants follow the signs of (x, y, z). For example, in the first octant (XOYZ), all coordinates are positive (+, +, +), while in the fifth octant below it, z becomes negative (+, +, -).
Is 3D geometry in Class 11 different from Class 12?
Yes. Class 11 introduces basic coordinate representation, distance, and section formulas in 3D. Class 12 builds directly on this by introducing lines, planes, direction cosines, and vector algebra.
How do I find the distance of a point from the coordinate planes?
The distance of a point P(x, y, z) from the XY plane is |z|, from the YZ plane is |x|, and from the ZX plane is |y|.
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