Class 12 Mathematics — Chapter 11: Three Dimensional Geometry
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 11, "Three Dimensional Geometry", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Three Dimensional Geometry" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Three Dimensional Geometry, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Three Dimensional Geometry (Class 12 Mathematics)
This chapter studies lines and planes in space using direction cosines and ratios, and finds angles and distances between them.
- Direction cosines & ratios
- Direction cosines l, m, n satisfy l² + m² + n² = 1; direction ratios are proportional to them.
- Equation of a line
- A line through a with direction b is r = a + λb (vector form); the Cartesian form uses (x−x₁)/a = (y−y₁)/b = (z−z₁)/c.
- Equation of a plane
- A plane has the form r·n̂ = d (normal form) or ax + by + cz = d, where (a, b, c) is the normal direction.
- Angle between objects
- Angles between two lines, two planes, or a line and a plane are found from their direction ratios / normals using the dot product.
- Distance
- Shortest distance between skew lines and the distance of a point from a plane are computed with vector formulae.
Key formulas — Three Dimensional Geometry
💡 Exam tips for Three Dimensional Geometry
- Reduce every problem to direction ratios and a point — then the standard formulae apply directly.
- For the angle between a line and a plane, use sinθ (between line and normal it is cosθ) — don't confuse the two.
Sample questions
Direction cosines of x-axis:
Along i-direction.
Line through point a with direction b:
Vector form, λ ∈ R.
Angle between two lines with direction vectors u, v:
Dot product formula.
Three Dimensional Geometry — FAQs
What are the key concepts in Class 12 Mathematics Three Dimensional Geometry?+
This chapter studies lines and planes in space using direction cosines and ratios, and finds angles and distances between them. Key ideas include Direction cosines & ratios, Equation of a line, Equation of a plane, Angle between objects, Distance.
What does Class 12 Mathematics Chapter 11 (Three Dimensional Geometry) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Three Dimensional Geometry" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Three Dimensional Geometry" questions free to practise?+
Yes — sign in with Google to practise "Three Dimensional Geometry" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Three Dimensional Geometry" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Practise all 66 questions free
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