# DC Pandey Units and Dimensions, Vectors Solutions

DC Pandey Mechanics Part 1 ‘Units, Dimensions and Vectors’ Solutions include all the fundamentals related to the scalar and vector quantities along with the derivation of dimensions. In this chapter of DC Pandey Solutions, you will learn about concepts like the dot product, cross product, commutative laws, associative laws, unit vectors and more such topics. Once you engage with the chapter you will develop a firm understanding of addition of vectors with respect to the geometric format, laws of vector products, magnitude determination of vectors and conversion of angle measures.

The chapter has two different sections with a total of three exercises. All the exercise questions aim at polishing your understanding of the chapter and helping you have a thorough revision of the same. The questions revolve around the fundamentals of different mathematical operations that can be performed on vectors, unit vector notations and dimension derivations. The questions are also essential from a competitive exam perspective, as they have been picked carefully according to the exam pattern and the probability of similar questions to appear in the upcoming papers.

Instasolv’s DC Pandey Mechanics Part 1 Solutions for ‘Units, Dimensions and Vectors’ covers every single aspect from the chapter and every question has been dealt with individually with vivid explanations. There are a lot of tricks which you can learn to enhance your performance in competitive exams like IIT, JEE and NEET. We, at Instasolv, promote a fruitful and engaging learning plan which will reduce the exam pressure and increase your confidence and level of preparation. With the guidance of our expert team, nothing can come in your way of scoring high and achieving all your aspirations and goals.

**Important topics for DC Pandey Mechanics Part 1 Solutions Chapter 2: Units, Dimensions and Vectors**

**Vectors **

In Chapter 2 of DC Pandey Physics Solutions, you will learn about vectors. Vectors are quantities which have a magnitude and a direction. In this chapter, you will learn about different components of vectors, scalar multiplication of vectors, equivalent vectors, analysis of vectors and vector magnitudes from the graph.

You will also learn to perform addition and subtraction on vector quantities. The chapter includes questions where you will have to perform these operations in an algebraic as well as graphic manner.

**Unit Vector Notations **

In this chapter, you will be introduced to this term – Unit Vector Notation. The angles denoted as α, β and γ are formed by the vector with the coordinates of x, y and z-axis. This is termed as the unit vector notation.

**Scalar and Vector Products **

Vectors can be multiplied in two different ways namely scalar products and vector products. When we find the product of magnitudes of two vectors along with the cosine of the angle that exists between them, the product is known as a scalar product.

On the other hand, when we find the product of magnitudes of two vectors with the sine of the angle between them, it is known as the vector product.

**Dimensions **

In this chapter, you will learn to derive the dimensions of various physical quantities with the help of their mathematical formula. Dimensions are basically the powers to which that fundamental quantity (like work, force, energy, speed or time) can be raised in order to represent the quantity. You need to first write down the formula of the quantity you are about to derive the dimensions for. Then you are required to substitute the components of the formula with the fundamental quantities like mass, length or time.

Use abbreviations to denote those terms in a square bracket and the resultant power along with the abbreviation will be your final answer. This topic is very important from the point of view of competitive as well as board exams.

**Exercise-wise Discussion of DC Pandey Mechanics Part 1 Chapter 2: Units, Dimensions and Vectors**

**Section I **

- This section begins with the exercise ‘Single Correct Option’ which has 56 questions.
- All of these questions require you to simplify the given formulas by substituting them with their SI Units and solving them further to obtain the condensed final answer.
- These formulas include angular momentum, velocity gradient, friction and resistance.
- There are other questions based on vectors applied in case of magnetic field intensity, speed and work.
- You will also find trigonometry based logical problems with respect to the fundamentals of scalar and non-scalar quantities. You will also utilize the fundamentals of vector products and scalar triple products in the exercise.
- Then, there is one ‘Match the Column’ question where you have to match the vector products with the formulas.

**Section II**

**The second section of DC Pandey Mechanics Part 1 ‘Units, Dimensions and Vectors’ includes 26 ‘Subjective Questions’**

- These questions include logical, analytical, application-based, theoretical, direct formula-based and reasoning questions.

- Basically the exercise presents an amalgam of all kinds of important problems from the chapter.

- These questions deal with concepts like a dimensionless constant, dot product, cross product, angle between vectors in different directions, sine law and power equations.
- You will also encounter questions where you will have to convert angles from degrees to radians and vice versa.

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- At Instasolv, we make sure that all the solutions are formulated in a simple language with detailed step by step explanations.
- Our DC Pandey Mechanics Part 1 Solutions for Units, Dimensions and Vectors will help you in revising and preparing for your exams at one go.
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