[Maths Class Notes] on What is Vector? Pdf for Exam

If you have taken mathematics and physics in your higher education, there is a chapter that you need to learn. It is a vector. To know what a is a vector, you need to have clear concepts about both elementary maths and physics. While learning the concepts of vectors, you might find it a bit tough because it relates to the application of maths and physics. Make sure to go through your books to learn all the concepts of vectors and visit the site of to get the comprehensive notes that can help you develop an interest in the chapter and solve complicated numerical problems.

Vector: Definition

Any object that has a magnitude and direction can be called a vector. If you are curious to know what a vector is in maths, remember that in mathematics, a vector deals with the problems that relate to different components.

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You can geometrically draw a vector easily as it is just a line segment with a directional arrow. As per the laws of mathematics, the length of the line is termed as the magnitude, and the arrow showing the direction.

Identicality of a Vector

Any vector can be considered identical with another if the direction and magnitude are the same for both. No matter where you shift a vector from the couple it remains identical to the other. However, you need to remember that this theory applies only if you do not change the vector’s direction.

In the above example, both the vectors have the property known as velocity and force. Both of them have a proper direction. The direction of the vector is related to its magnitude and the magnitude is again related to the speed.

Problems on Vectors

The problems that you need to do with vectors are addition, subtraction, multiplication, and transformation. You can learn adding and subtracting two to three vectors at first and then move to multiplication. The most interesting problem on the vector can solve a unit vector to a scalar.

Two-way multiplication is also possible with vectors where you can either multiply one vector with another or a scalar. Moreover, there are specific technical multiplications like the cross and dot product.

You should understand the concepts of vectors properly while you theoretically study them in physics. Detailed notes can be found on the site of . The experienced teachers at can help you to understand the procedures of solving the problem.

Vectors and Dimensions

As vectors have properties like magnitude and direction, it can have more than one dimension, you would be able to solve the sums with three dimensions. The dimensional vectors are quite advanced and you can study them in college if you pursue college courses in physics and maths.

Addition and Subtraction of Vectors

The process of addition, subtraction, and multiplication of vectors are mentioned here in brief.

Addition of a Vector:

if a vector is [vec{a}], the scalar will be [lambda].

Now if [vec{lambda}] has a positive direction then we can add up the lengths of [lambda] and [vec{lambda}]. In this situation, we can either compress or stretch the vector. By changing the position of the Lamda following the line segment.

You can also add the vectors even if the [lambda] is negative. All you need to do is hold the opposite vector. The concept of the opposite can only be clear to you if you study the vector chapter from the initial stage.

Subtraction of a Vector:

The vector subtraction is just the opposite of addition with vectors. Even if the vector has a magnitude it will have a negative direction. When you subtract a vector with a negative variable you can find it easier as it resembles the subtraction of scalar numbers.

Applications of Vector

As far as the application of vectors is concerned, you can use it to determine the speed and velocity of one moving body with the relation to the other. You can expect to get sums that relate to moving trains, space movements of particles.

You might not be able to solve the sums of vectors if you do not have a proper concept of motion, velocity, directions, and time.

Solved Examples

Q1. How to denote the magnitude of a vector?

Answer: To denote the magnitude of a vector you need to first address a vector. Suppose for a vector ‘c’, you can rite its magnitude to be |c|. In some maths books, you can find double bar mods such as ||c||.

Q2. By which theorem can you determine the magnitude of a vector?

Answer. To determine the magnitude of the vector, you will have to apply the Pythagorean Theorem.