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# RS Aggarwal Class 12 Chapter 24 Solutions (Vector or Cross Product of Vectors)

RS Aggarwal Solutions for Class 12 Chapter 24 ‘Vector or Cross Product of Vectors’ have been created to give you assistance in practising the exercise questions of this chapter. In this chapter, you will be introduced to the cross product of two vectors and the direction of the resultant. Other important topics that are covered in this chapter include the right-hand thumb rule, the physical representation of vectors and properties exhibited by the vector product of the given two vectors.

There are 26 exercise questions compiled together in one exercise in this chapter. These are a diverse variety of questions that are put together to give you enough questions for practising before your exams. If you go through the questions, you will find that every question possesses a unique challenge or in-depth knowledge of various topics related to vectors, angles between them and parallel lines.

The exercises of RS Aggarwal Solutions for Class 12 Chapter 24 ‘Vector or Cross Product of Vectors’ must be used as a mandatory add-on to your course textbook if you aim to achieve excellent marks in your school exams. Solving these exercises will also help you in various topics of your physics syllabus as well.

## Introduction to Cross Product of Vectors

If you have two vectors a and b and you intend to find their vector or cross product, then the magnitude of the vector product will be given as |a||b|sin such that 180° and is the angle between the two vectors. Now, the direction of the resultant vector after taking the cross product will be perpendicular to the vectors a and b and is represented by the unit vector n. All three vectors will have a right-handed orientation.

The right-handed orientation of the given two vectors and their cross product would refer to the case that when vector a is rotated in the direction of vector b then the direction of the resultant unit vector n will be as compared to a right-handed screw that would be rotated in a similar manner. You should note the point that a and b are non-null and non-parallel vectors. The direction of the resultant vector can be roughly given by the right-hand thumb rule.

Physical Representation of Vectors

If we consider a parallelogram with adjacent sides described by the vectors a and b and the angle between these adjacent sides be given as. Then the cross product of the vectors a and b will give the area of the parallelogram, that is,

αreα of the parallelogram=α X b=|α||b|sinθ

Properties of Vector Product

• The cross product of two vectors do not exhibit commutative property, because of α X b=-(b X α)
• (kα) X b=k(α X b)= α X (kb) is true in case of cross multiplication.
• If two vectors are collinear, i.e., =0, then sin=0. Making the cross product 0, i.e., α X b= 0.
• Cross product of two same vectors is equal to 0.
• If a = The
• Distributive law holds true in case of the vector product of vectors.

Highlights of the Chapter:

• a X b =
• αreα of the parallelogram=α X b=|α||b|sinθ

### Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 24 – Vector or Cross Product of Vectors

1. In the exercise solutions of 24A, you will learn the relationship between angles and direction of the resultant vectors after taking the cross product.
2. Other questions include proving that given vectors are collinear, finding the area of a parallelogram whose adjacent sides are represented by vectors, finding the area of a triangle whose vertices are given by vectors, finding unit vectors and many more.
3. You will also find very complex problems simplified in the exercise solutions of RS Aggarwal Class 12 Chapter 24.
4. These questions will give an appropriate idea of the pattern of questions asked in the board exams and the national level competitive exams such as JEE or BITSAT exams.

### Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 24 by Instasolv

1. The features of RS Aggarwal Class 12 Maths Solutions by Instasolv include simple language, detailed answers, compliant to the Board and many more.