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Introduction to Three Dimensional Geometry

ICSE · Class 11 · Mathematics

Complete topic list for Introduction to Three Dimensional Geometry in ICSE Class 11 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

59 questions30 flashcards5 concepts

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A basic representation of the three-dimensional Cartesian coordinate system showing the X, Y, and Z axes intersecting at the origin.
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4 Topics · ICSE Class 11 Mathematics

Topics in Introduction to Three Dimensional Geometry

1

1. Basic Ideas of 3D Coordinate System

  • A point in a plane has two coordinates.
  • A point in space has three coordinates.
  • The coordinates of a point in space are the perpendicular distances of the point from the three coordinate planes.
2

2. Feet of Perpendiculars and Reflections

  • The feet of perpendiculars from P(x,y,z) on the coordinate planes are D(x,y,0), E(0,y,z), and F(x,0,z).
  • The feet of perpendiculars from P(x,y,z) on the coordinate axes are A(x,0,0), B(0,y,0), and C(0,0,z).
  • The reflection of a point in a coordinate plane is its mirror image in that plane.
3

3. Octants and Location of Points

  • The coordinate axes in 3D divide space into eight octants.
  • The octants are numbered I to VIII using roman numerals.
  • The sign pattern of coordinates determines the octant.
4

4. Distance Formula and Distances from Axes

  • The distance between two points in space is found using the 3D distance formula.
  • The formula is a direct extension of the 2D distance formula.
  • The distance formula is derived using a rectangular parallelepiped and Pythagoras theorem.

Key Concepts

Central concept: Three-dimensional coordinate geometry describes points, planes, axes, distances, octants, reflections, and dividing points in space using ordered triples and standard formulas.

Three-dimensional rectangular coordinate systemCoordinates of a point in spacePoints on coordinate planes and axesFeet of perpendicularsOctantsReflection of a point in a coordinate planeDistance from coordinate axesDistance formula in 3D

Frequently Asked Questions

What are the important topics in Introduction to Three Dimensional Geometry for ICSE Class 11 Mathematics?
Key topics in Introduction to Three Dimensional Geometry include Three Dimensional Geometry Concept Map, Three Dimensional Geometry Concept Map, Three Dimensional Geometry Concept Map. These are the concepts ICSE Class 11 examiners draw on most — study them first, then practise related questions.
How to score full marks in Introduction to Three Dimensional Geometry — ICSE Class 11 Mathematics?
Understand the core concepts first, then work through the 59 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Introduction to Three Dimensional Geometry

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