Three-Dimensional Geometry
Class 12 3D Geometry — direction cosines, lines in space, planes, angles, distances and skew lines. Solved examples and MCQ tests for CBSE and ISC.
Study by topic — one focused page each
Direction Cosines & Direction Ratios
Every line in space points in a definite direction , and the cleanest way to record that direction with numbers is through its direction cosines . If …
Start this topic → 2Equation of a Line in Space
A straight line in space is completely fixed by two pieces of information: one point on it and one direction along it. Both the vector and the Cartesi…
Start this topic → 3Angle Between Lines & Shortest Distance
Once lines are written as "point plus direction", every relationship between two of them is governed by their direction vectors and . Two questions do…
Start this topic → 4The Plane
A plane is a flat, two-dimensional surface that extends without bound. In three dimensions a plane is pinned down the moment you fix its orientation (…
Start this topic →Chapter-wide tests
Online Test
10 MCQ • 20 min
IMO / Olympiad Practice
Olympiad level • 20 min
📝 Full Chapter Test (Download & Print)
35 marks • 75 min • with answer key