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Introduction to Three Dimensional Geometry — Revision Notes

ICSE · Class 11 · Mathematics

Introduction to Three Dimensional Geometry revision notes for ICSE Class 11 Mathematics: 4 topics in quick points.

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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Key Topics to Revise

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.

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Full Notes

Key Concepts

Three mutually perpendicular lines in spaceA point in space has threePoints on the xyThe equations of the coordinate planesThe three coordinate axes divide space

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 Basic Ideas of 3D Coordinate System, Feet of Perpendiculars and Reflections, Octants and Location of Points, Distance Formula and Distances from Axes. Study these first, then practise questions on each for Class 11 exams.
How should I revise Introduction to Three Dimensional Geometry for Class 11 exams?
Learn the core ideas first, then work through the 59 practice questions on Introduction to Three Dimensional Geometry. Revise 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.

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All ICSE Class 11 Mathematics Revision Notes

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