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Class 11 Mathematics — Chapter 12: Introduction to Three Dimensional Geometry

66 practice questions · 22 Easy · 22 Medium · 22 Hard

Practise Class 11 Mathematics Chapter 12, "Introduction to 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.

"Introduction to 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 Introduction to 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 11 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.

Key concepts: Introduction to Three Dimensional Geometry (Class 11 Mathematics)

This chapter introduces coordinates in three dimensions, the distance between points, and the section formula in space.

3D coordinate system
Three mutually perpendicular axes (x, y, z) locate a point by an ordered triple (x, y, z).
Octants
The three coordinate planes divide space into eight octants, distinguished by the signs of the coordinates.
Distance formula
Distance between (x₁,y₁,z₁) and (x₂,y₂,z₂) is √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²].
Section formula
The point dividing a segment in ratio m:n has coordinates found by the 3D section formula.
Midpoint
The midpoint is the average of the corresponding coordinates of the endpoints.

Key formulas — Introduction to Three Dimensional Geometry

Distance (3D)
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]
Section formula
[(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n), (mz₂+nz₁)/(m+n)]

💡 Exam tips for Introduction to Three Dimensional Geometry

  • The 3D distance formula just extends the 2D one with a z-term — don't drop the third coordinate.
  • For the midpoint, use ratio 1:1 in the section formula.

Sample questions

Q1Easy

Number of octants in 3D:

A.8✓ correct
B.4
C.6
D.2
Why

Three axes divide space into 8 regions.

Q2Medium

Distance between (1,2,3) and (1,2,5):

A.2✓ correct
B.3
C.4
D.5
Why

Only z differs by 2.

Q3Hard

Point dividing (1,2,3),(7,8,9) in ratio 2:1 internally:

A.(5,6,7)✓ correct
B.(3,4,5)
C.(4,5,6)
D.(7,8,9)
Why

((2·7+1·1)/3, ...) = (5,6,7).

Introduction to Three Dimensional Geometry — FAQs

What are the key concepts in Class 11 Mathematics Introduction to Three Dimensional Geometry?+

This chapter introduces coordinates in three dimensions, the distance between points, and the section formula in space. Key ideas include 3D coordinate system, Octants, Distance formula, Section formula, Midpoint.

What does Class 11 Mathematics Chapter 12 (Introduction to Three Dimensional Geometry) cover on XamBaaz?+

It covers 66 NCERT-aligned MCQs on "Introduction to 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 "Introduction to Three Dimensional Geometry" questions free to practise?+

Yes — sign in with Google to practise "Introduction to Three Dimensional Geometry" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.

How should I revise "Introduction to 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.

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