3D Geometry Class 12 – Best Questions for Board Exam Practice
Updated for CBSE 2025 | Practice the most important 3D Geometry questions with solutions
Chapter 11 of Class 12 Mathematics – Three-Dimensional Geometry – is a scoring and concept-rich topic. It covers lines, planes, angles, and distances in 3D space and is frequently asked in board exams. Below is a curated list of high-quality questions tailored for CBSE Class 12 Board Practice.
Exam-Oriented Practice Questions from 3D Geometry
2i - j + k.
L₁: r = (2i + 3j) + λ(i - 2j + k)L₂: r = (i - j + 4k) + μ(3i + j)
3x - y + 2z = 10.
r = (i + 2j) + λ(2i - j + k) and r = (3i - j) + μ(i + 4j - 2k) are skew and find their shortest distance.
Mixed Question Set – For Daily Practice
- Find the unit vector in the direction of vector
3i - 4j + 12k. - Find the equation of the plane which passes through the point (2, 1, -3) and is perpendicular to the vector
5i - 2j + 4k. - If a line has direction cosines
l, m, nand passes through origin, write its vector equation. - Find the coordinates of the foot of the perpendicular from point (1, 2, 3) on the plane
x + 2y + 2z = 9. - Find the angle between the line and the plane:
Line:r = (i + j + k) + λ(i - 2j + 2k)
Plane:2x - y + z = 5
Board Exam Tips for Scoring Full Marks in 3D Geometry
- Always convert vector equations to Cartesian form and vice versa — questions are often asked in both formats.
- Label every step and justify the use of formulas like dot product, cross product, and direction cosines.
- Practice sketching 3D positions of lines and planes to improve visualization.
- Make a formula sheet and revise it daily during exam prep week.
Final Thoughts
3D Geometry in Class 12 isn’t just about solving problems — it’s about understanding space. These handpicked board-level questions are aimed at developing both your accuracy and speed. Practicing them thoroughly will give you the confidence to tackle any 3D Geometry problem in the board exam.
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