CBSE Class 12 Maths Chapter-11 Important Questions - Free PDF Download
FAQs on Important Questions for CBSE Class 12 Maths Chapter 11 - Three Dimensional Geometry 2024-25
1. What are the major types of important questions that appear from Three Dimensional Geometry in CBSE Class 12 exams?
Key types include direction ratio/direction cosine problems, equations of lines and planes (vector and Cartesian forms), finding angles between lines and planes, distance between skew lines or between points and planes, and proof-based HOTS questions involving intersection, coplanarity, and shortest distances. These questions align directly with the CBSE 2025–26 blueprint and often carry varied marks based on complexity.
2. How can a student maximize marks in long answer (4–5 mark) questions on Three Dimensional Geometry?
To score full marks, students should:
- Organize solutions in a clear, step-wise manner including proper use of vector or Cartesian forms as required.
- State relevant formulas before applying them and show every calculation step, as CBSE follows step marking.
- Draw diagrams wherever possible to visualize lines, planes or intersections.
- Explicitly address all subparts, like points of intersection, angles, or distance values in the final answer.
- Highlight final answers and check units where applicable.
3. Which conceptual mistakes commonly appear in important board questions from Three Dimensional Geometry?
Frequent mistakes include:
- Confusing direction ratios with direction cosines.
- Incorrect use of formulas for distance between skew lines or point-to-plane distances.
- Assuming lines/planes are parallel or intersecting without verification.
- Skipping key vector/determinant steps in proof questions.
- Forgetting to check if a point truly lies on a given line or plane.
4. Why are HOTS (Higher Order Thinking Skills) questions important in Three Dimensional Geometry for CBSE Class 12?
HOTS questions test deeper conceptual understanding and logical application of multiple 3D geometry concepts. They require innovative thinking across formulas, transformations, and spatial reasoning, and they help students stand out in the top scoring range by showing analytical and problem-solving abilities valued by CBSE evaluators.
5. What is the usual board marks weightage for Three Dimensional Geometry in the CBSE Class 12 Mathematics paper (2025–26)?
This chapter typically carries 8–10 marks in total. The weightage is generally split between 1–2 short answer questions (1–2 marks each) for direct applications, and 1–2 long answer (4–5 mark) questions focusing on derivations, proofs, or HOTS problems, in alignment with the CBSE syllabus blueprint.
6. How can you distinguish whether two lines in space are skew, intersecting, or parallel in exam questions?
First, check the proportionality of direction ratios. If they are proportional and a common point exists, the lines are coincident; if only ratios match but no point coincides, they are parallel. Lines are skew if they neither intersect nor are parallel. To test for intersection, simultaneously solve both line equations for a possible common point.
7. What are effective strategies for selecting which important questions to practice for CBSE 2025–26 board exams in Three Dimensional Geometry?
Prioritize:
- Stepwise practice of NCERT examples and exercises for coverage of fundamentals.
- Previous years’ board and sample questions to spot recurring patterns.
- HOTS and long-answer questions involving multiple concepts (like intersection or coplanarity).
- Key formula-based questions for direction ratios/cosines, equations of lines and planes, and shortest distance problems.
8. How are direction cosines and direction ratios essential in Three Dimensional Geometry important questions?
Direction cosines (l, m, n or cos α, cos β, cos γ) specify the orientation of a line or plane relative to the axes, while direction ratios are unnormalized direction numbers. Many board questions involve converting between ratios and cosines for calculations of angles, lines, and distances, making them central to the chapter.
9. What are common traps examiners use in Three Dimensional Geometry questions, and how can students avoid them?
Examiners may:
- Mix up vector and Cartesian forms unexpectedly.
- Test calculation of distances in non-standard orientations.
- Add extra or irrelevant information (like unnecessary points or conflicting ratios) to distract students.
10. What is a systematic approach to prove collinearity or to find the plane equation through three points in board questions?
Let points be A(x₁, y₁, z₁), B(x₂, y₂, z₂), C(x₃, y₃, z₃). Use the determinant:
| x−x₁ y−y₁ z−z₁ |
| x₂−x₁ y₂−y₁ z₂−z₁|
| x₃−x₁ y₃−y₁ z₃−z₁| = 0
If this equals zero, points are collinear; if not, expand to get the required plane’s Cartesian equation as per board expectations.
11. How does practicing previous year important questions help strengthen exam performance in Three Dimensional Geometry?
Practicing past questions:
- Reveals often repeated and high-weightage topics.
- Improves familiarity with the format and marking expectations.
- Enhances speed, stepwise presentation, and accuracy under real exam conditions.
- Builds confidence in handling both direct and HOTS-style questions as per the current CBSE pattern.
12. What higher-order skills are needed for HOTS questions where lines and planes intersection in 3D Geometry is tested?
Skills needed include:
- Fluency in both vector and Cartesian forms.
- Ability to set up and solve systems representing intersections (using direction ratios and point coordinates).
- Mastery of determinant and vector product methods for proof and derivation-based answers.
- Logical sequencing and explicit justification of each calculation step, following the CBSE step-marking scheme.
13. What is an effective revision plan for Three Dimensional Geometry important questions just before the board exam?
Revise in this order:
- Start with NCERT solved examples and exercises.
- Move to concept-revision using recent previous year important questions.
- Practice HOTS, proofs, and multi-step problems most likely to be featured as long-answer items.
- In the final week, allocate time to formula quick-reviews and attempt full-length mock/test papers within exam time limits.
14. What are the best methods to calculate the shortest distance between two skew lines in board exam questions?
Use the vector formula:
Shortest distance, SD = |(a₂−a₁) · (b₁ × b₂)| / |b₁ × b₂|,
where a₁, a₂ are position vectors, and b₁, b₂ are direction vectors of the two lines. Write all cross product and dot product steps explicitly and simplify carefully to reach the final value.
15. Why is vector notation often preferred over Cartesian equations in certain Three Dimensional Geometry problems?
Vector notation offers a compact and general method for representing equations of lines and planes, simplifying operations like dot and cross product calculations. For exam problems involving direction or perpendicularity, vectors make it faster and easier to apply relevant theorems without translating between multiple coordinate variables.

















