NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1 Vector Algebra - PDF Download

1. Some Basic Concepts

Vector - A quantity that has magnitude as well as direction is called a vector. It is represented by a directed line segment. Vector is denoted by $\overrightarrow{\mathrm{AB}}$ . The point A from where the vector $\overrightarrow{\mathrm{AB}}$ starts is called its initial point, and the point B where it ends is called its terminal point. The distance between initial and terminal points of a vector is called the magnitude (or length) of the vector, denoted as $|\overrightarrow{\mathrm{AB}}|$, or $|\vec{a}|$ , or a. The arrow indicates the direction of the vector. 

Position Vector - Consider a point P in space, having coordinates (x, y, z) with respect to the origin O(0, 0, 0). Then, the vector $\overrightarrow{\mathrm{OP}}$ having O and P as its initial and terminal points, respectively, is called the position vector of the point P with respect to O.

Direction Cosines - Lets say the position vector $\overrightarrow{\mathrm{OP}}($ or $\vec{r})$ of a point P(x, y, z). The angles α, β, γ made by the vector $\vec{r}$ with the positive directions of x, y and z-axes respectively, are called its direction angles. The cosine values of these angles, i.e., cosα, cosβ and cos γ are called direction cosines of the vector $\vec{r}$ and usually denoted by l, m and n, respectively. 

2. Types of Vectors

Zero Vector - A vector whose initial and terminal points coincide, is called a zero vector (or null vector). It is denoted as $\overrightarrow{0}$ . Zero vector has a zero magnitude.

Unit Vector - A vector whose magnitude is unit is called unit vector. The unit vector in the direction of a given vector $\vec{a}$ is denoted by $\hat{a}$ . 

Coinitial Vectors - Two or more vectors having the same initial point are called coinitial vectors.

Collinear Vectors - Two or more vectors are said to be collinear if they are parallel to the same line, irrespective of their magnitudes and directions.

Equal Vectors - Two vectors $\vec{a}$ and $\vec{b}$ are said to be equal, if they have the same magnitude and direction regardless of the positions of their initial points, and written as $\vec{a}=\vec{b}$ .

Negative of a Vector - A vector whose magnitude is the same as that of a given vector (say, $\overrightarrow{\mathrm{AB}}$ ) , but direction is opposite to that of it, is called negative of the given vector.

Tips for Solving Exercise 10.1 Class 12 Chapter 10 Differential Equations

Ex 10.1 class 12 maths ch 10 has simple questions that can be solved if you understand the concepts precisely. For solving these questions our subject experts of eSaral have combined some useful tips which you can check below.

1. Students should first learn the basic terms and concepts of vector algebra for better understanding of questions asked in ex 10.1.

2. In ex 10.1 class 12 maths solutions, you must be well-versed with different types of vectors like zero vector, unit vector, coinitial vectors etc. and position vector, direction cosines.

3. There are some examples before exercise, you should solve them for comprehend the concepts clearly.
   

Importance of Solving Ex 10.1 Class 12 Maths Chapter 10 Differential Equations

There are numerous benefits of solving questions in NCERT solutions for class 12 maths chapter 10 ex 10.1 Differential Equations.

1. NCERT solutions for ex 10.1 class 12 maths chapter 10 are solved in step by step and detailed format by the experts of eSaral for preparing exams in a more productive way.

2. All the basic concepts related to vector algebra and types of vectors are elaborated in simple language by our experienced teachers of eSaral that will be beneficial for you in solving questions asked in exams.

3. NCERT solution PDFs available here will also help you to cross check your answers.

4. If you practice questions in NCERT solutions class 12 maths chapter 10 ex 10.1. This will help you in remembering the concepts properly.
   

Frequently Asked Questions

Question 1. Define vectors?

Answer 1. A quantity that has magnitude as well as direction is called a vector. Vector is denoted by $\overrightarrow{\mathrm{AB}}$ . 

Question 2. What is a zero vector?

Answer 2. A vector whose initial and terminal points coincide, is called a zero vector (or null vector). It is denoted as $\overrightarrow{0}$ . Zero vector has a zero magnitude.

Question 3. What are coinitial vectors?

Answer 3. Two or more vectors having the same initial point are called coinitial vectors.