NCERT Solutions for Class 12 Mathematics Chapter 10 Vector Algebra

NCERT Solutions for Class 12 Mathematics Chapter 10 - Vector Algebra

Welcome to the Chapter 10 - Vector Algebra, Class 12 Mathematics NCERT Solutions page. Here, we provide detailed question answers for Chapter 10 - Vector Algebra. The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.

Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics Vector Algebra and excel in their exams. By going through these Vector Algebra question answers, you can strengthen your foundation and improve your performance in Class 12 Mathematics. Whether you’re revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.

Exercise 1

Q 1:

Represent graphically a displacement of 40 km, 30° east of north.

\begin{align}Here, vector\;\overrightarrow{OP}\; represents \;the\; displacement\; of \;40\; km, 30° East \;of \;North.\end{align}

Q 2:

Classify the following measures as scalars and vectors.

(i) 10 kg (ii) 2 metres north-west (iii) 40°

(iv) 40 watt (v) 10^–19 coulomb (vi) 20 m/s²

(i) 10 kg is a scalar quantity because it involves only magnitude.

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

(iii) 40° is a scalar quantity as it involves only magnitude.

(iv) 40 watts is a scalar quantity as it involves only magnitude.

(v) 10^–19 coulomb is a scalar quantity as it involves only magnitude.

(vi) 20 m/s² is a vector quantity as it involves magnitude as well as direction.

Q 3:

Classify the following as scalar and vector quantities.

(i) time period (ii) distance (iii) force

(iv) velocity (v) work done

(i) Time period is a scalar quantity as it involves only magnitude.

(ii) Distance is a scalar quantity as it involves only magnitude.

(iii) Force is a vector quantity as it involves both magnitude and direction.

(iv) Velocity is a vector quantity as it involves both magnitude as well as direction.

(v) Work done is a scalar quantity as it involves only magnitude.

Q 4:

In Figure, identify the following vectors.

(i) Coinitial (ii) Equal (iii) Collinear but not equal

\begin{align} (i) \;Vectors\; \overrightarrow{a}\; and\; \overrightarrow{d}\; are \;coinitial\; because\; they\; have\; the\; same \;initial \;point. \end{align}

\begin{align}(ii)\; Vectors\;\overrightarrow{b} \;and\;\overrightarrow{d}\; are\; equal\; because\; they\; have\; the\; same \;magnitude \;and\; direction. \end{align}

\begin{align}(iii)\; Vectors\;\overrightarrow{a} \;and\; \overrightarrow{c} \;are\; collinear\; but\; not\; equal\;. This\; is\; because\; although\; they\; are \;parallel,\; their\; directions\; are\; not \;the\; same.\end{align}

Q 5:

Answer the following as true or false.

\begin{align}(i) \overrightarrow{a}\; and\; \overrightarrow{-a}\; are\; collinear.\end{align}

(ii) Two collinear vectors are always equal in magnitude.

(iii) Two vectors having same magnitude are collinear.

(iv) Two collinear vectors having the same magnitude are equal.

(i) True.

\begin{align}(i) \overrightarrow{a}\; and\; \overrightarrow{-a}\; are\; collinear.\end{align}

(ii) False.

Collinear vectors are those vectors that are parallel to the same line.

(iii) False.

It is not necessary for two vectors having the same magnitude to be parallel to the same line.

(iv) False.

Two vectors are said to be equal if they have the same magnitude and direction, regardless of the positions of their initial points.

Frequently Asked Questions about Vector Algebra - Class 12 Mathematics

- 1. How many questions are covered in Vector Algebra solutions?
- All questions from Vector Algebra are covered with detailed step-by-step solutions including exercise questions, additional questions, and examples.
- 2. Are the solutions for Vector Algebra helpful for exam preparation?
- Yes, the solutions provide comprehensive explanations that help students understand concepts clearly and prepare effectively for both board and competitive exams.
- 3. Can I find solutions to all exercises in Vector Algebra?
- Yes, we provide solutions to all exercises, examples, and additional questions from Vector Algebra with detailed explanations.
- 4. How do these solutions help in understanding Vector Algebra concepts?
- Our solutions break down complex problems into simple steps, provide clear explanations, and include relevant examples to help students grasp the concepts easily.
- 5. Are there any tips for studying Vector Algebra effectively?
- Yes, practice regularly, understand the concepts before memorizing, solve additional problems, and refer to our step-by-step solutions for better understanding.

Exam Preparation Tips for Vector Algebra

The Vector Algebra is an important chapter of 12 Mathematics. This chapter’s important topics like Vector Algebra are often featured in board exams. Practicing the question answers from this chapter will help you rank high in your board exams.

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