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Introduction To Three- Dimensional Geometry

Telangana Open School (TOSS) · Class 12 · Mathematics

Complete topic list for Introduction To Three- Dimensional Geometry in Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

57 questions24 flashcards5 concepts

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4 Topics · Telangana Open School (TOSS) Class 12 Mathematics

Topics in Introduction To Three- Dimensional Geometry

1

Coordinate System and Coordinates of a Point in Space

  • Three mutually perpendicular lines X'OX, Y'OY, and Z'OZ form the coordinate axes, intersecting at origin O(0, 0, 0).
  • The three coordinate planes (XY, YZ, ZX) divide space into eight regions called octants.
  • The coordinates (x, y, z) of a point P are the perpendicular distances from P to the YZ, ZX, and XY planes respectively.
2

Distance Between Two Points in Space

  • The distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is calculated using an extended version of the Pythagorean theorem.
  • The formula is derived by constructing a rectangular parallelepiped with PQ as the diagonal.
  • Distance from origin to point P(x, y, z) is √(x² + y² + z²).
3

Section Formula in 3D

  • The coordinates of a point dividing the line segment joining P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) in the ratio m:n.
  • For internal division: ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n), (mz₂ + nz₁)/(m+n)).
  • For external division: ((mx₂ − nx₁)/(m−n), (my₂ − ny₁)/(m−n), (mz₂ − nz₁)/(m−n)).
4

Direction Cosines and Direction Ratios

  • Direction cosines (l, m, n) are cosines of angles α, β, γ that a line makes with positive X, Y, Z axes respectively.
  • l = cosα, m = cosβ, n = cosγ.
  • For any line: l² + m² + n² = 1.

Key Concepts

Central concept: Three-Dimensional Geometry

Coordinate System in SpaceDistance Between Two PointsSection Formula in 3DDirection Cosines and Direction RatiosProjection of Line SegmentsAngle Between Two Lines

Frequently Asked Questions

What are the important topics in Introduction To Three- Dimensional Geometry for Telangana Open School (TOSS) Class 12 Mathematics?
Introduction To Three- Dimensional Geometry covers several key topics that are frequently asked in Telangana Open School (TOSS) Class 12 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 — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 57 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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