CBSE Class 12 Maths Question Bank: Important Questions for Vectors & 3D Geometry 2026
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Preparing for the board exams can be a daunting task, especially when you are dealing with high-weightage units like Vectors and Three-Dimensional (3D) Geometry. As per the latest curriculum released for the 2025-26 academic session, this unit remains a cornerstone for students aiming for a 95+ score. With a combined weightage of 14 marks, mastering Direction Cosines, Lines, and Planes is non-negotiable.
This comprehensive guide serves as your ultimate CBSE Class 12 Maths Question Bank, focusing on the most repeated patterns, official resources, and expert-recommended strategies to ace your 2026 exams.
Importance of Vectors & 3D Geometry in CBSE 2026
In the current CBSE exam pattern, the "Vectors and 3D Geometry" unit is valued not just for its direct marks but for its application in competitive exams like JEE and CUET. In 2026, the board continues to emphasize competency-based questions, meaning you won't just solve for x, y, z; you will need to visualize the spatial orientation of lines and planes.
Weightage Breakdown
Vector Algebra: Focuses on dot and cross products.
3D Geometry: Focuses on direction cosines, equations of lines, and planes.
Total Marks: 14 (out of 80 theory marks).
Chapter-Wise Important Concepts: Direction Cosines, Line & Plane
To score high, you must move beyond rote memorization. Here are the core areas where the CBSE Class 12 Maths Question Bank typically draws its most challenging questions.
1. Direction Cosines and Direction Ratios
This is the foundation of 3D geometry. Most 1-mark and 2-mark questions are centered here.
Direction Cosines (l, m, n): Understanding the relationship l^2 + m^2 + n^2 = 1.
Direction Ratios (a, b, c): How to convert ratios into cosines using the magnitude of the vector.
Repeated Question Pattern: Finding the direction cosines of a line passing through two points (x1, y1, z1) and (x2, y2, z2).
2. Equations of a Line in Space
The board frequently asks for conversions between Vector and Cartesian forms.
Line through a point and parallel to a vector: r = a + \lambda b.
Line through two points: Understanding the denominator as the direction ratios of the line.
Shortest Distance: This is a "hot" topic for 5-mark or 6-mark questions. You must practice finding the distance between two skew lines.
3. The Plane (Standard and Intercept Forms)
While the syllabus has seen minor rationalizations, the following remain vital:
Normal Form of a Plane: r \cdot n = d.
Angle between two planes: Calculated using the dot product of their normal vectors.
Distance of a point from a plane: A frequent 3-mark question involving the perpendicular distance formula.
Analyzing Previous Years' Papers (2020–2025)
A deep dive into official previous year papers reveals that the board has a "favorite" set of problems. In the CBSE Class 12 Maths Question Bank, the following types of questions have appeared in 4 out of the last 5 years:
The Perpendicularity Condition: Proving two lines are perpendicular by showing a1 a2 + b1 b2 + c1 c2 = 0.
The Foot of the Perpendicular: Finding the coordinates of the foot of the perpendicular dropped from a point to a plane.
Image of a Point: Finding the image of a point with respect to a plane (often a 5-mark long answer).
Master List of Formulas
As per the requirement to focus on conceptual retention, here are the essential formula categories you must have on your fingertips:
Distance Formula (3D Space)
Section Formula (Internal and External Division)
Direction Cosines Identity
Vector Equation of a Line (One point & parallel vector)
Cartesian Equation of a Line
Shortest Distance between Skew Lines
Shortest Distance between Parallel Lines
General Equation of a Plane
Intercept Form of a Plane
Angle between two Lines (Cosine formula)
Angle between two Planes
Expert Preparation Tips for 2026
To rank high and secure top marks, follow this structured study plan:
NCERT First: 80% of the board paper is directly or indirectly based on NCERT examples and miscellaneous exercises. Do not skip the miscellaneous section!
Visualization: Use diagrams for every 3D Geometry problem. Visualizing the "Normal" to a plane helps in 90% of plane-related problems.
Time Management: Solve the 5-mark questions first. Vectors and 3D often take time due to lengthy calculations.
Practice Daily: Set a goal to solve at least 5 questions from the CBSE Class 12 Maths Question Bank specifically on "Shortest Distance" and "Foot of the Perpendicular."
Official Resources & Important Links
Official CBSE Academic Portal: Access Question Banks
Direct CBSE Question Bank Access: Download Class 12 PDFs
Maharashtra Board (MSBSHSE) SCERT: Official Question Bank Link
Conclusion
Mastering Vectors and 3D Geometry is a journey of moving from 2D thinking to spatial awareness. By focusing on Direction Cosines, understanding the nuances of Lines and Planes, and consistently practicing from the CBSE Class 12 Maths Question Bank, you are setting yourself up for success. Remember, in Mathematics, clarity of concept is the best shortcut to speed.
FAQ Section
Q1. Is the CBSE Class 12 Maths Question Bank enough for 100/100?
While a question bank provides a wide variety of problems, achieving a perfect score requires a thorough understanding of NCERT concepts combined with the practice of the CBSE Class 12 Maths Question Bank and at least 10 sample papers.
Q2. What is the most important topic in 3D Geometry for 2026?
Statistically, the "Shortest Distance between two skew lines" and "Equations of a Plane passing through the intersection of two planes" are the most high-yield topics.
Q3. How many marks are allocated to Vectors and 3D in 2026?
The unit carries a total of 14 marks. This usually consists of one 5-mark question, one 3-mark question, two 2-mark questions, and two 1-mark MCQs.
Q4. Where can I find the official CBSE 2026 Question Bank?
You can access official question banks and competency-based questions directly from the CBSE Academic website.
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