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Revision Notes

The Planes

Telangana Open School (TOSS) · Class 12 · Mathematics

Quick revision notes for The Planes — Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

54 questions25 flashcards5 concepts

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Key Topics to Revise

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.

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Full Notes

Key Concepts

The general equation of a planeIf a plane passes throughWhen a plane makes intercepts \(The normal form of a planeThe angle \( \theta \) between

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.

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