Find the best tutors and institutes for Class 12 Tuition
Q3(ii):
Classify the following as scalar and vector quantities.
(ii) distance
Solution :
1. Conceptual Definition of Scalar and Vector Quantities
To classify the physical quantity distance, we must adhere to the definitions established in Euclidean geometry and classical mechanics:
- Scalar Quantity: A physical quantity that possesses magnitude only and does not require a specified direction for its complete description [Scalar Field Theory].
- Vector Quantity: A physical quantity that possesses both magnitude and a defined direction in space, obeying the laws of vector addition [Parallelogram Law of Vectors].
2. Analysis of Distance
Distance is defined as the total path length covered by an object moving between two points. By definition:
- Magnitude: Distance is always a non-negative real number ($\text{distance} \geq 0$).
- Directional Independence: As an object traverses a path, the direction of motion may change continuously (e.g., in curvilinear motion). Distance tracks the cumulative length of the trajectory regardless of these changes in orientation [Kinematics fundamental principle].
3. Comparative Vector/Scalar Table
| Feature | Distance | Displacement |
|---|---|---|
| Definition | Total path length | Shortest change in position |
| Type | Scalar | Vector |
| Directionality | None | Required (Vector magnitude + direction) |
4. Visual Representation of Distance vs. Displacement
5. Final Conclusion
Since distance is a measure of total length traversed between two points without any inherent requirement for a directional vector component, it is mathematically classified as a scalar quantity.
Final Solution: Distance is a scalar quantity.
More Questions from Class 12 Mathematics Vector Algebra EXERCISE 10.1
- Q1: Represent graphically a displacement of 40 km, 30° east of north.
- Q2(i): Classify the following measures as scalars and vectors. (i) 10 kg
- Q2(ii): Classify the following measures as scalars and vectors. (ii) 2 meters north-west
- Q2(iii): Classify the following measures as scalars and vectors. (iii) 40°
- Q2(iv): Classify the following measures as scalars and vectors. (iv) 40 watt
- Q2(v): Classify the following measures as scalars and vectors. (v) $10^{-19}$ coulomb
- Q2(vi): Classify the following measures as scalars and vectors. (vi) $20$ m/s$^2$
- Q3(i): Classify the following as scalar and vector quantities. (i) time period
- Q3(iii): Classify the following as scalar and vector quantities. (iii) force
- Q3(iv): Classify the following as scalar and vector quantities. (iv) velocity
- Q3(v): Classify the following as scalar and vector quantities. (v) work done
- Q4(i): In Fig 10.6 (a square), identify the following vectors. (i) Coinitial
- Q4(ii): In Fig 10.6 (a square), identify the following vectors. (ii) Equal
- Q4(iii): In Fig 10.6 (a square), identify the following vectors. (iii) Collinear but not equal
- Q5(i): Answer the following as true or false. (i) $\vec{a}$ and $-\vec{a}$ are collinear.
- Q5(ii): Answer the following as true or false. (ii) Two collinear vectors are always equal in magnitude.
- Q5(iii): Answer the following as true or false. (iii) Two vectors having same magnitude are collinear.
- Q5(iv): Answer the following as true or false. (iv) Two collinear vectors having the same magnitude are equal.
CBSE Solutions for Class 12 Mathematics Vector Algebra
Chapters in CBSE - Class 12 Mathematics
Top Tutors who teach Vector Algebra
My students get acquainted with me easily... I will be both friendly and strict ( according to the need)... Students love to learn physics with me. Their learning process will be in easy and efficient. They will Excel in concepts and problem solving
She is very talented and knowledgeable tutor. She taught me 12th board CBSE Physics very well. She explained the concepts clearly even I asked multiple times. She is my motivator. Apart from her teaching, She is very friendly and has a fun motive. I have scored 95% in Physics. All my credits and thanks to her.
I teach Chemistry to students of Class 11 and Class 12 and have been working in the teaching field for the past 7 years. Chemistry has always been a subject that I am passionate about, and I enjoy helping students understand concepts clearly and perform confidently in academics as well as competitive examinations. My goal is to make Chemistry simple, logical, and interesting for students through structured and concept-focused learning. I hold a Master of Science (M.Sc.) degree in Chemistry, which has provided me with strong subject knowledge and a deeper understanding of various chemical concepts. My academic background helps me explain topics in a clear and systematic way so that students can easily understand and apply them while solving numerical and theoretical questions. Over the years, I have worked with students from different learning backgrounds and understanding levels. This experience has taught me the importance of adapting teaching methods according to the student’s requirements. I focus on helping students strengthen their conceptual understanding, improve their analytical and problem-solving skills, and gain confidence in handling Chemistry effectively for both board exams and competitive exams. My teaching methodology is structured, student-centric, and exam-oriented. I follow a well-planned lesson structure where topics progress step by step from basic to advanced levels. Before starting a new topic, I assess the student’s current understanding level so that I can explain concepts in the most effective manner. I also use suitable real-life examples to simplify complex chemical concepts and make learning more relatable and easier to understand. I strongly believe that conceptual clarity is more important than rote learning. During my classes, I encourage students to ask questions freely and clear doubts without hesitation. If a student finds a concept difficult, I patiently re-explain it multiple times until complete understanding is achieved. I also conduct regular revision sessions, exercise practice, and detailed discussions of previous years’ board and competitive examination questions to strengthen preparation and retention. I conduct both online and offline classes depending on the convenience of students. During my sessions, I use PPT presentations and whiteboard explanations to make learning more organized, visual, and engaging. My classes are interactive and focused on building confidence, helping students solve problems independently, and preparing them effectively for examinations. As a teacher, my aim is to help students develop a strong foundation in Chemistry and remove the fear many students have towards the subject. I believe that with the right guidance, regular practice, and conceptual understanding, every student can excel in Chemistry. Helping students improve academically and achieve success in their exams continues to motivate me in my teaching journey.
As per my son's experience, he clears all the concepts and teaches very well, explaining repeatedly until it is fully understood.
Hey Champions, I am Atul Pal, Love to do interaction with student pursuing the career in technological field. I had done my Bachelors of Technology In Electronics and Communication Engineering. I used to teach student since 2018, I had to teach the technical Subject like Physics, Mathematics and Python Programing Language. Right now I am working as a Python Developer in an MNC and having advance understanding about python.
Atul is a good teacher. He is very patient and repeats till the student understands the topic. Only issue is his tone of voice is flat and uninteresting and he has a heavy accent that sometimes makes it difficult for the student to understand certain words.
As an experienced teacher for 12 years, I have been teaching to make students interested in the subjects of Maths. My attitude is to help children improve in studies in the best possible way.
With a distinguished Doctorate in Chemistry, I bring 28 years of expertise, seamlessly integrating profound knowledge and unparalleled teaching prowess. As a Chemistry Teacher for CBSE and IBDP Chemistry Faculty, I've significantly contributed to intellectual growth in prestigious institutions like Kendriya Vidyalaya, Ecole Mondiale World School, and Singapore International School etc. Recognized as a trailblazer, I've served as an Assistant Examiner and Moderator for Internal Assessment in IBDP Chemistry for six years, upholding the highest evaluation standards and showcasing a deep understanding of curriculum intricacies. My extensive experiences beyond conventional teaching establish me as a luminary in Chemistry education, leaving an enduring legacy in the annals of education. I remain dedicated to inspiring future generations to achieve unparalleled heights in scientific inquiry and knowledge.
A very knowledgeable and caring teacher Patient and passionate teaching. All these qualities helped me succeed and score well in my board exams.
Other Subjects in CBSE - Class 12
Download free CBSE - Class 12 Mathematics Vector Algebra EXERCISE 10.1 worksheets
Download Now