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# Fundamentals of Physics Chapter 3 Solutions: Vectors

Halliday Resnick & Walker Fundamental of Physics Volume 1 Solutions for Chapter 3 ‘Vectors’ will explain to you everything about vectors and its components. The major concepts covered in this chapter of Resnick Halliday Walker include scalars, components of a vector, unit vector notation, geometrical addition of vectors, and the product of a scalar & vector. After understanding these concepts, you will be capable of adding vectors in head-to-tail arrangements by using the commutative and associative laws, subtracting two vectors, calculating the components of a vector on a given coordinate system, determining the magnitude and orientation of a vector, and converting angle measures between degrees and radians.

Resnick Halliday and Walker Fundamental of Physics Volume 1 Solutions for Chapter 3 ‘Vectors’ contains 1 exercise which is divided into 4 modules and has a total of 79 questions. All the questions cover important concepts of the chapter such as the addition of vectors, multiplication of vectors, unit vectors, angle conversions, and the magnitude of vectors, etc. If you want to give your best in the competitive exams like JEE and NEET, then it is necessary to get accustomed to the problems given in this chapter.

Instasolv gives you the solutions to all the questions provided in Resnick Halliday and Walker Physics Volume 1 Chapter 3. Our team of professionals has formed the appropriate answers for your IIT JEE exam preparation. You will be able to understand our solutions easily because our experts have explained every question step by step. Practising Instasolv’s solutions can also help you with some tricks to save a lot of time during competitive exams.

## Important Topics for Resnick Halliday & Walker Fundamentals of Physics Volume 1 Solutions Chapter 3: Vectors

Scalars: Scalars are the quantities that only have magnitude. For example, 15°C (temperature). Scalar quantities always obey the rules of the algebra.

Vectors: Vectors are the quantities that hold both magnitude and direction. For example, a displacement of (5 m, North). These quantities obey the rules of vector algebra.

Components of a Vector: A two-dimensional vector usually has 2 parts which are present in two different directions, horizontal and vertical. These are the two components of the vector which are given by ax= a cosθ and ay= a sinθ

Where θ is the angle made between the positive x-axis in the clockwise direction. These algebraic signs of the components of the vector indicate the direction of the associated axis. Given the components, you can find the magnitude and direction of the vector by using

Unit Vector Notation: The angles α, β, and γ formed by the vector with the three coordinate axes x, y, and z respectively are called the unit vector notation of a vector.

Geometrical Addition of Vectors: Two vectors can be added geometrically by drawing them to a common scale and placing them head to tail. The vector sum is the addition of the vector connecting the tail of the first to the head of the second.

Vector addition is commutative i.e.   and obeys the associative law i.e.

Adding Vectors in Component Form: To add vectors in component form, you can use the rules rx=ax+bx ,  ry= ay + by , rz = az+ bz . This way you can add the vectors and express the sum in unit-vector notation or magnitude-angle notation.

The Scalar Product: The scalar product of two vectors is also called the dot product. The scalar quantity is given by , where is the angle between the directions of a and b.  The scalar product obeys the commutative law.

The Vector Product: The vector product of two vectors is also called a cross product. The vector product of two vectors a and b is given by the formula

### Exercise Discussion of Halliday Resnick and Walker Fundamentals of Physics Volume 1 Solutions Chapter 3: Vectors

Module 1: Vectors and their components

The first module of the exercise contains 7 questions which are based on the topic of components of the vector. Some questions ask you to find components of a vector in a given direction, angles of a vector. You will also find a question where you need to express angles in radians.

Module 2: Unit vectors, adding vectors by components

The second module of the exercise contains 24 questions that cover topics like the magnitude of the vector, direction, and angle of a vector, sum of vectors in unit vector notation, angle of displacement, etc. The majority of the questions are about finding the magnitude of a vector in different directions and the sum of vectors.

Module 3: Multiplying Vectors

The third module of the exercise contains 11 questions based on the scalar or dot product of the vectors and vector or cross product. Some of the questions include finding scalar or vector products in a given direction and angle.