Updated for new NCERT 2026-2026 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.