Ncert Solutions Maths class 12th

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. 

Students can access and download the NCERT Solutions for Class 12 Vector Algebra in free PDF format from our website Shiksha.com. We provide the NCERT Solutions PDF for free for all the chapter of class 12th including the chapter 10 Vector algebra. Students can visit the below link to download the PDF;

• Chapter 10 Vector Algebra NCERT Solution PDF

Shiksha's NCERT Solutions for Class 12 Vector Algebra are designed by expert Math faculties. Our NCERT Vector Algebra Solutions provide step-by-step explanations for all NCERT textbook exercises. These Solutons covers topics of the chapter such as addition, scalar multiplication, and dot/cross products of 2 or morevector quantities. Students can use our NCERT Solutions of Vector Algebra for studying, practicing, and revising the concepts.

Shiksha provides solutions of class 11th and 12th chapters for all subjects NCERT textbooks. Our NCERT Solutions for Class 12 Differential Equations  and other chapter aligne with the latest CBSE 2025 syllabus and exam pattern. We aso provide additional information related to the chapter including importan topics, concepts, formulas, and weightae in different exams.

Class 12 Maths includes the chapter Differential Equations as a part of calculus unit. As per the formal NCER  Definition, A differential equation is an equation that contains one or more derivatives of a dependent variable with respect to one or more independent variables.

For example:

$\frac{dy}{dx}=3x+2$

Here, the derivative $\frac {dy} {dx}$ represents the rate of change of $y$ with respect to $x$, and the equation defines how this rate changes with $x$.