You are learning...

Chapter 11 Class 12 Three Dimensional Geometry

Click on any of the links below to start learning from Teachoo...

Updated for new NCERT 2024-2025 Edition.

 

Get NCERT Solutions of Class 12 3D Geometry, Chapter 11 Class 12 of the NCERT book. Solutions of all questions and examples with formula sheet explained.

 

In Class 11, we studied basics of Three Dimensional Geometry - Like Distance Formula, Section Formula

 

In this chapter, 3D Geometry of Class 12, we lean about 3 Dimensional Lines and Planes, and also find equations in vector form - using the help of Chapter 10 Vectors.

The specific topics include - 

  • Direction cosines and Direction Ratios - How to find using different methods - when angle is given, when side is given, when two points are given
  • Equation of Line - We form equation of line in different cases - one point and 1 parallel line, 2 points given. We also learn how to convert vector form of equation to Cartesian form
  • Angle between two lines - We find Angle between two lines using Vector formula, Cartesian Formula, Using Direction Cosines and Ratios
  • Shortest Distance between two lines - Finding shortest distance between two parallel and two skew lines
  • Equation of plane - Finding equation of plane in normal form, when perpendicular and point passing through is given, when passing through 3 Non Collinear Points. We also find equation of plane using intercept form, and when plane is passing through intersection of planes
  • Coplanarity of 2 Lines - Checking if 2 lines are coplanar
  • Angle between two planes - Finding angle between two planes using Vector and Cartesian method
  • Distance between point and plane - Both Vector and Cartesian Formula
  • Angle between Line and Plane - Vector formula only
  • Equation of line under planes condition - Finding Equation of line when some condition between two planes are given
  • Point with Lines and Planes - Finding coordinates of point when line crosses through a plane or Finding point where line and plane intersect

To learn more, click on any topic of concept wise or do NCERT Exercise way.

Serial order wise

  Ex 11.1
  Ex 11.2
  Examples
  Miscellaneous
  Case Based Questions (MCQ)
  Plane

Concept wise

  Direction cosines and ratios
  Equation of line - given point and //vector
  Equation of line - given 2 points
  Angle between two lines - Vector
  Angle between two lines - Cartisian
  Angle between two lines - Direction ratios or cosines
  Shortest distance between two skew lines
  Shortest distance between two parallel lines
  Equation of plane - In Normal Form
  Equation of plane - Prependicular to Vector & Passing Through Point
  Equation of plane - Passing Through 3 Non Collinear Points
  Equation of plane - Intercept Form
  Equation of plane - Passing Through Intersection Of Planes
  Coplanarity of 2 lines
  Angle between two planes
  Distance of point from plane
  Angle between Line and Plane
  Equation of line under planes condition
  Point with Lines and Planes

What's in it?

Updated for new NCERT 2024-2025 Edition.

 

Get NCERT Solutions of Class 12 3D Geometry, Chapter 11 Class 12 of the NCERT book. Solutions of all questions and examples with formula sheet explained.

 

In Class 11, we studied basics of Three Dimensional Geometry - Like Distance Formula, Section Formula

 

In this chapter, 3D Geometry of Class 12, we lean about 3 Dimensional Lines and Planes, and also find equations in vector form - using the help of Chapter 10 Vectors.

The specific topics include - 

  • Direction cosines and Direction Ratios - How to find using different methods - when angle is given, when side is given, when two points are given
  • Equation of Line - We form equation of line in different cases - one point and 1 parallel line, 2 points given. We also learn how to convert vector form of equation to Cartesian form
  • Angle between two lines - We find Angle between two lines using Vector formula, Cartesian Formula, Using Direction Cosines and Ratios
  • Shortest Distance between two lines - Finding shortest distance between two parallel and two skew lines
  • Equation of plane - Finding equation of plane in normal form, when perpendicular and point passing through is given, when passing through 3 Non Collinear Points. We also find equation of plane using intercept form, and when plane is passing through intersection of planes
  • Coplanarity of 2 Lines - Checking if 2 lines are coplanar
  • Angle between two planes - Finding angle between two planes using Vector and Cartesian method
  • Distance between point and plane - Both Vector and Cartesian Formula
  • Angle between Line and Plane - Vector formula only
  • Equation of line under planes condition - Finding Equation of line when some condition between two planes are given
  • Point with Lines and Planes - Finding coordinates of point when line crosses through a plane or Finding point where line and plane intersect

To learn more, click on any topic of concept wise or do NCERT Exercise way.