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Introduction to Three Dimensional Geometry

Madhya Pradesh Board · Class 11 · Mathematics

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

162 questions48 flashcards5 concepts

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4 Topics · Madhya Pradesh Board Class 11 Mathematics

Topics in Introduction to Three Dimensional Geometry

1

1. Coordinate Axes, Coordinate Planes, and Octants

  • Three mutually perpendicular lines intersect at the origin O and are called the x-axis, y-axis, and z-axis.
  • The three coordinate planes are XY-plane, YZ-plane, and ZX-plane.
  • The XY-plane is taken as the plane of the paper and the z-axis is perpendicular to it.
2

2. Coordinates of a Point in Space

  • A point P in space is written as P(x,y,z).
  • For point P(x,y,z), x, y, and z are the perpendicular distances from the YZ-plane, ZX-plane, and XY-plane respectively.
  • A point in space corresponds to one ordered triplet (x,y,z).
3

3. Distance Between Two Points in Space

  • The distance formula in three dimensions is an extension of the two-dimensional distance formula.
  • For points P(x1,y1,z1) and Q(x2,y2,z2), the distance is found using the square root of the sum of squares of the differences of corresponding coordinates.
  • The derivation uses two right triangles and the Pythagorean theorem twice.
4

4. Worked Examples and Important Results

  • Example 2 type questions ask for the octant from the signs of coordinates.
  • (-3,1,2) lies in the second octant.
  • (-3,1,-2) lies in octant VI.

Key Concepts

Central concept: Three dimensional coordinate geometry describes the position of points in space using three coordinates with respect to three mutually perpendicular coordinate planes and axes.

Coordinate system in spacex-axis, y-axis, z-axisXY-plane, YZ-plane, ZX-planeOriginOctantsCoordinates of a point in spaceSpecial positions of pointsDistance between two points in space

Frequently Asked Questions

What are the important topics in Introduction to Three Dimensional Geometry for Madhya Pradesh Board Class 11 Mathematics?
Introduction to Three Dimensional Geometry covers several key topics that are frequently asked in Madhya Pradesh Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Introduction to Three Dimensional Geometry — Madhya Pradesh Board Class 11 Mathematics?
Understand the core concepts first, then work through the 162 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.

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