Vector Algebra

(i) Time period involves only magnitude. So, it is scalar quantity.

(ii) Distance involves only magnitude. So, it is scalar quantity.

(iii) Force involves both magnitude and direction. So, it is vector quantity.

(iv) Velocity involves both magnitude and direction. So, it is vector quantity.

(v) Work done involves only magnitude. So, it is scalar quantity.

(i) 10kg involves only magnitude. So, it is scalar quantity.

(ii) 2 meters north-west involves both magnitude and direction. So, it is vector quantity.

(iii) 40⁰  involves only magnitude. So, it is scalar quantity.

(iv) 40⁰  watts involves only magnitude. So, it is scalar quantity.

(v) 10^-19 coulomb involves only magnitude. So, it is scalar quantity.

(vi) 20m/s^-2 involves magnitude and direction. So, it is vector quantity.

$40km,30^0$ east of north.

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. 

Class 12 Vector Algebra consists of several important topics for not only class 12 board exams but also varous competitive exams. Check the several key topics of the chapter below;

• Types of Vectors: Unit, Position, Co-initial, collinear, and coplanar vectors
• Operations on Vectors:  Addition, subtraction, and Dot & Cross multiplication.
• Properties of cross-product: Geometric interpretation, Area of a parallelogram, Triangle

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.