3D Geometry Class 12 Notes – All Formulas, Concepts & JEE Tips
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eSaral provides detailed Notes of Physics, Chemistry, Mathematics, and Biology for classes 11 and 12. So here you will get class 12 notes for mathematics. There are important points in Mathematics, such as formulae, equations, identities, properties, theorems, etc., what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET, and Board Examinations. 3D Geometry Class 12 Notes to prepare for boards and JEE. With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 12 Maths. These Notes have been designed in the simplest and most precise format, covering almost all the Domains like Differential Calculus, Algebra, Trigonometry, and Coordinate Geometry. These Notes will also be helpful to those who are preparing for competitive Exams like JEE.
India's Best Exam Preparation for Class 12th - Download Now
3D Geometry Class 12 Notes
India's Best Exam Preparation for Class 12th - Download Now
India's Best Exam Preparation for Class 12th - Download Now
India's Best Exam Preparation for Class 12th - Download Now
India's Best Exam Preparation for Class 12th - Download Now
India's Best Exam Preparation for Class 12th - Download Now
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Frequently Asked Questions
Find answers to common questions.
What is the difference between direction cosines and direction ratios?
Direction cosines (l, m, n) are the cosines of the angles a line makes with the three coordinate axes, and they satisfy l² + m² + n² = 1. Direction ratios (a, b, c) are any three numbers proportional to the direction cosines. Direction cosines are unique (up to sign), while direction ratios are not unique for a given line.
How many marks does 3D Geometry carry in CBSE Class 12 Boards?
3D Geometry carries approximately 10–12 marks in CBSE Class 12 Board exams. The chapter typically includes one 5-mark question (on lines or planes) and two shorter questions of 2–3 marks each. Based on the CBSE marking scheme, this makes it one of the higher-weightage chapters in the Geometry unit.
What are the most important topics in 3D Geometry for JEE Main?
The most important topics in 3D Geometry for JEE Main are the shortest distance between skew lines, the equation of a plane (all forms), the distance of a point from a plane, and the angle between a line and a plane. These four topics together account for nearly 70–80% of all 3D Geometry questions asked in JEE Main between 2019 and 2024.
How do you find the shortest distance between two skew lines?
Two lines in 3D that are neither parallel nor intersecting are called skew lines. The shortest distance between them is found using the formula d = |(a₂ − a₁) · (b₁ × b₂)| / |b₁ × b₂|, where a₁, a₂ are position vectors of points on each line and b₁, b₂ are their direction vectors. This formula appears almost every year in JEE Main.
Do I need to know 3D Geometry for JEE Advanced?
Yes, 3D Geometry is part of the JEE Advanced syllabus as well. JEE Advanced questions tend to be more conceptual and may combine 3D Geometry with vector algebra or calculus. Topics like coplanarity, image of a point in a plane, and angle bisectors of planes are more likely to appear in JEE Advanced than in JEE Main.
Is 3D Geometry difficult for JEE Main?
3D Geometry is moderately difficult for JEE Main. The concepts are straightforward, but the large number of formulas and the need to switch between vector and Cartesian forms makes it tricky under exam conditions. Students who practise 30–40 previous year questions and keep a dedicated formula sheet consistently score full marks on this chapter