NCERT

There are important topics in Class 12 Linear Programming which are asked in the CBSE 12 Boards. Class 12 Board questions are from important topics such as linear programming problems (LPP), graphical method of solving LPPs, feasible region, bounded/unbounded solutions, and corner point method. Class 12 Linear Programming is asked for around  4-6 mark in CBSE board exams.

Students can use these steps for downloading the PDF for 3D Geometry NCERT Solutions given below;

• Visit the Official Page: Chapter 11 Three dimensional Geometry Solutions
• Access the Solutions and Scroll down to download PDF
• Click on "Download Free PDF"
• Save the PDF in their device

NCERT Solutions for 3D Geometry serves as a mathematical foundation developer for all the students. All competition exam aspirant must use NCERT Textbooks and its solutions for better understanding for fundamental concepts in 3D Geometry. Having a proper understanding of foundation knowledge of chapter is important for competitive exams like JEE and NEET. 

There are various reasons to use Shiksha's NCERT Solutions for 3D Geometry. Students can use 3D Geometry class 12 maths Solutions for various purposes like practice, revision, and making notes. These solutions follow the latest CBSE 2025 syllabus and NCERT textbook pattern. Shiksha Solutions for 3D Geometry are accurate and provide step-by-step explanations of all the questions.

Students must know that question papers are prepared on the basis of NCERT Textbook and its questions. Students can practice NCERT Maths Textbooks for most repeated questions of 3D Geometry. Mostly questions are asked based on direction cosines, finding angles between lines, the shortest distance between skew lines, and equations of planes are frequently repeated.

3D Geometry holds good weightage in the class 12 board exams, So students must be aware of the important topics that can be asked in the exams. Class 12  Three Dimensional Geometry chapter covers many important topics like direction cosines and ratios, equations of a line, angles between two lines, skew lines, the shortest distance, and equations of planes. Students can use our NCERT Solutions for Class 12 3D Geometry for clear understanding of these topics.

The Magnitude of a vector by providing clear, step-by-step explanations using both algebraic formulas and geometric interpretation. For a vector? = xi? + yj? + zk? , the magnitude is calculated as:

$|\vec {a}| = \sqrt {x^2 + y^2 + z^2}$

Shiksha's NCERT Solutions provides explanation for various other concepts including vector projections, unit vectors, and real-world applications. 

NCERT Solutions for Class 12 Vector Algebra are prepared by our experts. Our NCERT SOlutions are fully updated according to the latest CBSE 2025 syllabus. NCERT Vector Algebra solutions cover all the revised textbook exercises, including essential concepts like types of vectors, magnitude and direction, dot and cross products, and vector applications in 3D space. Our Solutions provides step-by-step explanations for all the questions, Students can use these solutions as a reliable resource for board exam preparation as well as for competitive exams like JEE and CUET UG.

As per the NCERT Textbooks, An orthogonal triad in vector algebra is a 3D cordinate point system where three vectors that are mutually perpendicular to each other, meaning the angle between each pair of vectors is 90°. These vectors are typically non-zero, linearly independent, and often form the basis of 3D space like the i? , j? , k? unit vectors in the Cartesian coordinate system.

Yes, Shiksha's NCERT Solutions for Class 12 Vector Algebra do cover the concept of orthogonal triads, We have used this concept specially while explaining dot product, cross product, and geometric interpretation of vectors.