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Chapter 11 Class 12 Three Dimensional Geometry

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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.

Concept wise

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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.