Skip to main content
Super TutorResources
Chapter 27 of 31
Syllabus

The Planes — Syllabus

Telangana Open School (TOSS) · Class 12 · Mathematics

What The Planes covers in Telangana Open School (TOSS) Class 12 Mathematics: 4 topics, for the 2026-27 session.

54 questions25 flashcards7 formulas & key relations5 concepts

Interactive on Super Tutor

Studying The Planes? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for syllabus and more.

Try Super Tutor — Free

Free trial, no card needed.

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

Topics in The Planes

1

General Equation of a Plane

  • The general equation of a plane is \( ax + by + cz + d = 0 \), where \( a, b, c \) are not all zero.
  • This equation represents a plane because any point satisfying it lies on a flat surface extending infinitely.
  • If two points lie on a plane, the line joining them also lies entirely on the plane.
2

Equation of a Plane Through a Given Point

  • If a plane passes through a point \( (x_1, y_1, z_1) \), its equation is \( a(x - x_1) + b(y - y_1) + c(z - z_1) = 0 \).
  • Here, \( a, b, c \) are direction ratios of the normal to the plane.
  • Infinitely many planes can pass through a single point since a, b, c can vary.
3

Equation of a Plane Through Three Points

  • A unique plane passes through three non-collinear points.
  • The determinant form is used: \( \begin{vmatrix} x - x_1 & y - y_1 & z - z_1 \\ x_2 - x_1 & y_2 - y_1 & z_2 - z_1 \\ x_3 - x_1 & y_3 - y_1 & z_3 - z_1 \end{vmatrix} = 0 \).
4

Intercept and Normal Forms of a Plane

  • Intercept form: \( \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 \), where a, b, c are intercepts on x, y, z axes.
  • Normal form: \( lx + my + nz = p \), where l, m, n are direction cosines of normal and p is perpendicular distance from origin.

Key Concepts

Central concept: The Plane

General Equation of a PlaneEquation of Plane Through a PointPlane Through Three PointsIntercept Form of PlaneNormal Form of PlaneAngle Between Two PlanesDistance from Point to PlaneAngle Bisector Planes

Work through every topic in The Planes with notes and quizzes

Start This Chapter

Frequently Asked Questions

What are the important topics in The Planes for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in The Planes include General Equation of a Plane, Equation of a Plane Through a Given Point, Equation of a Plane Through Three Points, Intercept and Normal Forms of a Plane. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise The Planes for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 54 practice questions on The Planes. 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.

More resources for The Planes

All Telangana Open School (TOSS) Class 12 Mathematics Syllabus

For serious students

Get the full The Planes chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for Telangana Open School (TOSS) Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free