🧮 Mathematics

3D Geometry Questions

Practise 3d geometry for Class 11-12 with timed rounds, instant feedback and difficulty that adapts as you play.

Class levels covered

∞

Fresh questions each round

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Mathematics

What is 3d geometry?

Three-dimensional geometry describes points, lines and planes in space using direction ratios, direction cosines and vector or Cartesian equations.

Why it matters

It underpins engineering drawing, computer graphics and physics, and carries steady marks in Class 12 board and entrance papers.

Key concepts you will practise

Direction cosines and direction ratios
Equation of a line in space (vector and Cartesian form)
Equation of a plane and the angle between planes
Shortest distance between skew lines

Tips that save marks

Convert every question to vector form first — the formulas are shorter.
Check whether two lines are parallel, intersecting or skew before applying a distance formula.

Question bank by class level

Class 11-12 · Senior secondaryGenerated each round

Start practising 3D Geometry

Frequently asked questions

What is the difference between direction ratios and direction cosines?

Direction ratios are any numbers proportional to the components of a direction; direction cosines are those components normalised so the sum of their squares is 1.

How do I find the shortest distance between two skew lines?

Take the cross product of the two direction vectors, then project the vector joining a point on each line onto that cross product.