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Introduction To Three- Dimensional Geometry — Syllabus

Telangana Open School (TOSS) · Class 12 · Mathematics

What Introduction To Three- Dimensional Geometry covers in Telangana Open School (TOSS) Class 12 Mathematics: 4 topics, for the 2026-27 session.

57 questions24 flashcards13 formulas & key relations5 concepts

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4 Topics · Telangana Open School (TOSS) Class 12 Mathematics · 2026-27

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

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Frequently Asked Questions

What are the important topics in Introduction To Three- Dimensional Geometry for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Introduction To Three- Dimensional Geometry include Coordinate System and Coordinates of a Point in Space, Distance Between Two Points in Space, Section Formula in 3D, Direction Cosines and Direction Ratios. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Introduction To Three- Dimensional Geometry for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 57 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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