Chapter 11 • Class 12 Mathematics
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
1
Direction Cosines & Direction Ratios
A line in space has a direction. The direction cosines of a line are the cosines of the angles that it makes with the positive , , axes, written . The…
Start this topic → 2Equation of a Line in Space
A line is fixed by a point on it and a direction. Vector form The line through point with direction is Cartesian (symmetric) form Through with directi…
Start this topic → 3Angle Between Lines & Shortest Distance
With two lines given by their direction vectors, two natural quantities arise: the angle between them and (if they do not meet) the shortest distance.…
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