JEE Main is one of the toughest competitive exams and therefore requires immense practice and hard work. Scoring consistent marks in all three subjects will help an aspirant secure a good rank in the upcoming JEE Main 2023. Vectors are a crucial topic in the JEE math and physics exams.
It is a relatively easy topic to comprehend. Therefore, with regular practice and a good understanding of the concepts, you master vectors. This blog is a comprehensive guide on vectors JEE Mains questions and their importance in the JEE Main examination.
Is Vector Maths Important for JEE Mains?
Vector is an important topic for the JEE Main maths examination. A quantity with both magnitude and direction is a vector. We need to be familiar with the rules to use vector algebra.
Every year, one can expect one or two questions on this topic. The topic vector is common for both maths and physics. Hence, understanding it thoroughly will help you score full marks in vector questions from both sections.
In contrast to algebra, vectors are more of a geometrical concept. We, therefore, recommended students visualize the concepts while discussing.
The important topics of vector algebra in the JEE Main are
- Vectors and scalars.
- Addition of vectors.
- components of a vector in two-dimensional and three-dimensional space.
- Dot product and cross product.
- Scalar and vector products.
- Scalar and vector triple product.
Vectors Physics Weightage in JEE Mains
Vectors are important for physics as well. Every year you can expect at least one question from the vector. It’s a relatively easy topic. With conceptual understanding and some amount of practice, you can easily score well in this section.
It includes concepts such as vector addition, subtraction, scalar multiplication, dot product, cross product, and many more. These concepts find use in the later sections of kinematics, mechanics, and other areas of physics and mathematics. Therefore, scoring well in this section will boost your overall score in the JEE Main exam.
The chapter, vector is included in the grade 11 syllabus, and you learn about this topic initially during the JEE preparation. Most of the students do not face many issues while understanding the concepts of vectors or solving numerical problems..
But students tend to forget the concepts sometimes because of a lack of practice. Hence, make it a point to practice and revise problems from this section before your exams.
Some of the important topics in this section are
- Scalars and vectors.
- Vector addition and subtraction.
- Zero vector.
- Scalar and vector products.
- Unit Vector.
- Resolution of a Vector.
Vectors JEE Mains Notes
J. Willard Gibbs (1839–1903), is popularly known as the Father of Vector Algebra. His thorough research and findings served as the foundation for the development of vector algebra and vector analysis.
A vector quantity is a physical quantity that contains magnitude and direction. We can depict vectors with a direct, pointed line. The length shows the vector’s magnitude, while the orientation depicts the vector’s direction.
On the other hand, scalars are defined as quantities that can only be depicted using their magnitude. Examples that are frequently used include mass, work, distance, speed, etc.
Examples of vector quantities are force, momentum, acceleration, displacement, and velocity. So, it is reasonable to infer that a vector is a directed line segment with a specific magnitude and direction.
Let us understand the different types of vectors.
Co-initial Vectors
When two or more different vectors share the same initial points, we call them co-initial vectors. This type of vector originates from the same location.
Collinear Vectors
Collinear vectors are two or more vectors, regardless of their size or direction, that are parallel to one another. Since they are parallel, they never come into contact with each other.
Zero Vectors
A zero vector is a vector with 0 magnitudes and an undefined direction. In physics and mathematics, zero vectors are important because they provide a reference point for other vectors.
Unit Vector
We refer to a vector with a magnitude of one as a unit vector.
Position Vector
A position vector is a vector that represents the position of a point relative to an origin or reference point. It is also known as a displacement vector or a radius vector.
Coplanar Vectors
Three or more vectors in the same plane are said to be coplanar vectors. Two independent vectors that are occasionally found in the same plane, are known as coplanar vectors.
Unlike and Like Vectors
In physics and mathematics, vectors are those vectors that have the same magnitude and direction.
Unlike vectors, which are a set of vectors that have different directions or magnitudes. For example, if two vectors have the same length but point in different or opposite directions, they are considered, unlike vectors.
Equal Vectors
When two or more vectors have the same magnitude and direction, they are called equal vectors.
Displacement Vector
The displacement vector represents the change in the position of an object from one point to another. A displacement vector is a line that connects the initial point to the final point. The length here is the magnitude of the displacement.
Negative Vector
A negative vector is a type of vector in which both vectors have the same value but is pointing in opposite directions.
Product of Two Vectors
Dot Product
The magnitude of the two vectors and the cosine angle between them results in the vector dot product. For instance, the dot product is A, if the magnitude of vectors A and B is |A||B| and the angle between the vectors is cos. B = [A][Bcos].
A.B. is the dot product, |A| is the magnitude of vector A, |B| is the magnitude of vector B, and cos is the cosine angle in the middle of the two vectors.
This formula shows the magnitude and the angle combined. The value of the dot product could be zero in some circumstances.
Vector Products
The magnitude of the two vectors and their sine angle combine to form the vector product of the two vectors.
For instance, if the two vectors have the values A and B, their magnitude is |A||B|, and their sine angle is sin. AxB=|A|||B|Sin is the formula for the cross-products of two vectors.
Right-Hand Vector product Rule
The right-hand vector product rule highlights the direction of the cross-product of two vectors. According to this rule, we must extend the right index finger in the direction of the first vector (A) and the middle finger in the direction of the second vector (B).
The orientation of the cross product will therefore be indicated by the thumb of the hand (AxB).
FAQ: Vectors JEE Mains Questions
JEE questions on vectors class 11 vector previous year questions
Please refer to the solved papers from ExamSIDE for practicing vector questions for JEE.
Vectors JEE Mains Questions PDF
You may refer to JEE Main website vector practice questions PDF.
Vectors previous year JEE questions Physics PDF
This is a very good PDF for physics vector JEE Main questions.
Is vector important for JEE Physics?
Yes, the vector is an important concept for Physics in JEE Mains. It requires less effort and thus you can achieve a full score in the vector questions with proper practice and understanding. This topic is common in both physics and maths.
Hence, with a good conceptual understanding, you can answer questions from both sections.
Conclusion
The topic vectors hold significant importance in the JEE Main syllabus and are considered to be relatively easy. It is a common topic that finds its application in both physics and mathematics, making it a scoring section in the exam.
To score full marks in the vector section, it is essential to have a thorough understanding of the underlying concepts and practice numerous numerical problems. With consistent practice and a strong grasp of the concepts, you can easily master this topic and confidently solve any question that comes your way.
We hope this blog helps you with the vector JEE Main questions. Do let us know your specific query regarding vectors in the comments below.
