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The Planes

Telangana Open School (TOSS) · Class 12 · Mathematics

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

54 questions25 flashcards5 concepts

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

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

Frequently Asked Questions

What are the important topics in The Planes for Telangana Open School (TOSS) Class 12 Mathematics?
The Planes 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 The Planes — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 54 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.

More resources for The Planes

All 31 chapters — Telangana Open School (TOSS) Class 12 Mathematics Syllabus

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