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# RD Sharma Class 12 Maths Solutions Chapter 25 - Vector or Cross Product ## RD Sharma Solutions for Class 12 Maths Chapter 25 - Vector or Cross Product - Free PDF Download

RD Sharma Class 12 Chapter 25 Vector or Cross Product Solutions is given here. In this chapter, students will learn how to calculate the vector product of two vectors, the vector product when two vectors are given in the cartesian form and the use of vector product in geometrical applications. RD Sharma Class 12 Solutions Vector or Cross Product PDF is provided in a detailed way here so that students can access all the solutions in the same pattern and sequence as in the RD Sharma textbooks.

Last updated date: 22nd May 2023
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## Class 12 RD Sharma Textbook Solutions Chapter 25 - Vector or Cross Product

Consider a and b as two non-zero parallel vectors. The cross product of two vectors a and b is defined only in three-dimensional space and it is denoted by a×ba×b. The Vector is also known as Cross Product.

Vector Product is defined by the following formula:

$a \times b = \left | a \right | \left |b \right |\sin(\theta )n a \times b = \left | a \right | \left |b \right |\sin(\theta )n$

Where |a||a| is the modulus of aa. It is also known as the magnitude of aa

$\left |b \right | \left |b \right |$  is the modulus of bb

θθ is the angle between two vectors aa and bb, and nn is a unit vector

### Following Are The Properties of Vector Product

1. Vector product does not follow the commutative rule. It is given by

$a \times b = -(b \times a)a\times b = -(b \times a)$

1. Vector multiplication rule

$(ka) \times b = k(a \times b) = a \times(kb)(ka)\times b = k(a\times b) = a \times (kb)$

1. If the given vectors are collinear then a×b=0a×b=0

(Since the angle between both the vectors would be 00, then the value of $\sin(0)=0\sin(0)=0$)

1. a×ba×b in terms of unit vectors can be represented as

$a = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j}a = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j}$

$b = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j}b = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j}$

$a \times b = ( a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j})( b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j}) a \times b = ( a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j})( b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j})$

1. Vector product follows distributive laws

$a \times (b + c) = (a \times b) + (a \times c) a \times (b +c) = (a \times b)+(a \times c)$

### Solutions For The Class12 Rd Sharma Maths Chapter 25 Vector Or Cross Product Is Available For A Free Download In A PDF File Format

Chapter 25th of the Class 12 RD Sharma Math book is Vector or Cross Product. And to ace in this Chapter students require a good amount of practice in solving the questions from this Chapter. Because the more practice of the Chapter 25 Vector or Cross Product a student does the better, they become. Solving the questions develops the various skills in the students helpful for the final Class 12 exam, such as it decreases the time taken for solving a single question, also it helps in increasing the accuracy of solving the question. And these two skills are the most important ones for the exam.

But along with solving the questions, it is just as important for the students to know that they have solved all the questions of Chapter 25 Vector or Cross Product in a manner it was supposed to be solved, and for that, the students of Class 12 requires the solutions for the Chapter 25 Vector or Cross Product nd hence Vedantu provides the students with the complete solutions for the RD Sharma Class 12, Chapter 25 Vector or Cross Product, which is available for a free download in a PDF file format for all the Class 12 students.

Also, if you are looking for the solutions of the next Chapter which is Scalar Triple Product you can find it here: RD Sharma Class 12 Math Solutions Chapter 26 - Scalar Triple Product ()

### Benefits Of Having The Solutions For The Rd Sharma Class 12, Chapter 25 Vector or Cross Products

The solutions of RD Sharma Class 12, Chapter 25 Vector or Cross Product helps the students in many ways, some of which are listed below:

• It helps the students in comparing their answers for the Chapter 25 Vector or Cross Product with the one given in the solutions, which in turn helps the students in measuring their progress.

• It helps the students in understanding the steps to solve the question, which they find rather difficult to solve in particular.

• The solutions for the RD Sharma Class 12, Chapter 25 Vector or Cross Product boosts the morale of the students. Because when the students know that if they are stuck on some questions, they can find a way out, motivating them to try and attempt all the given questions.

• It helps the students of Class 12 in overall understanding of the RD Sharma Chapter 25 Vector or Cross Product. And also, it gives the students a way to solve the questions in as simple a manner as possible.

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• It is Available in PDF: One of the crucial things for the students is to have the solutions in a way that it becomes easy to access and does not necessarily require the students to have internet all the time, and hence Vedantu provides the Solutions in a PDF file format, which can be accessed anytime and anywhere.

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## FAQs on RD Sharma Class 12 Maths Solutions Chapter 25 - Vector or Cross Product

1. What is the vector product of two vectors?

The vector product of two vectors is a vector perpendicular to both of them. Its magnitude is calculated by multiplying its magnitudes by the sine of the angle between them.

2. Does cross-product obey commutative law?

The cross product of two vectors does not obey commutative law.

3. What are the applications of vector products?

Following are the applications of vector product

1. It is used to find a vector that is perpendicular to two given vectors

2. It is used to find the area of a parallelogram.

3. It is used to find the volume of a parallelepiped

4. What should I do if I find some questions of RD Sharma Class 12, Chapter 25 Vector or Cross Product, difficult to solve?

In the RD Sharma Class 12, Chapter 25 Vector or Cross Product there are many questions given, which covers all the topics of the Chapter. Hence, it is understandable that students may find a few questions rather difficult to solve from the exercise of RD Sharma Class 12, Chapter 25 Vector or Cross Product. In such cases, students can use solutions for understanding the concepts and then solve the questions once again by themselves. Also, you can find the solutions for the said Chapter here at Vedantu.

5. Why should I download the solutions for the RD Sharma Class 12, Chapter 25 Vector or Cross Product, that Vedantu provides?

The first thing which is a must for all the solutions is that it has to be easily understandable, and the same goes for the RD Sharma Class 12, Chapter 25 Vector or Cross Product. Hence, Vedantu provides the solutions in such a simplified manner that it becomes extremely easy for the students to comprehend and grasp them. And since it is solved by the expert educators of the Math subject there is a trust factor attached to it. Furthermore, it is available for a free download in a PDF File so that all the Class 12 students can use it.