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Why Vectors in Mathematics Are So Much Important?

Why Vectors in Mathematics Are So Much Important?

by Purva Jagtap

 The vectors in mathematics are considered to be the object that will be having the direction as well as magnitude in them. The magnitude will always help in defining the size of the vector and it will be represented by a line with an arrow where the length of the line is considered to be the magnitude of the vector and the arrow will always help in showing and displaying the direction of the vector. This is also known as the Euclidean vector or simply the term vectors.

 Two kinds of vectors will always be said to be of equal length if the magnitude and direction are always the same and the best benefit is that it will help in playing a very important role in the world of mathematics, physics as well as engineering. As per vector algebra vector can be very easily added to another vector and the order of the addition of two vectors will never matter because the result will ultimately be very much the same and accurate.  Apart from all the above-mentioned points, it is also very much important for the kids to enrol themselves on platforms like Cuemath online so that they have a good command over the concept of vectors and scalars.

 The vector is also considered to be the mathematical structures in which they will be fulfilling different kinds of applications in the world of physics very easily. The location of points on the coordinate plane can be represented with the help of coordinates and the usage of the vector will further help in simplifying the overall process of 3-D geometry very well. Along with the term vector the individuals also need to learn the term scalar which will be helping in terms of representing the real numbers and vector and scalar are normally used together. The very common example of the vector will be acceleration, force, increase or decrease in temperature, velocity and several other kinds of things. Hence, it is very much important for people to calculate the things in vector form so that they can have quantity as well as direction side-by-side that will help in making different kinds of decisions very easily. 

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The vector will always have magnitude as well as direction which are considered to be its rotation. The magnitude of the vector will be shown by vertical lines and it will be representing the length of the vector. Mathematically this is found with the help of the Pythagoras theorem and different kinds of vectors are also very easily available in the whole industry. Unit vector will be the one whose length will be is equal to 1 and the zero vectors are the one which has the magnitude of zero. Different kinds of operations can even be performed on the vectors like vector addition which will help in joining the head to tail, vector Subtraction that will further help in dealing with the things perfectly, scalar multiplication in which the vector by a scalar quantity will be multiplied and the term will be referred to as scaling. The magnitude of the vector is changed but the direction will never change in this particular case. The scalar Triple product is considered to be a box product or the mixed triple product of these vectors and it will include the product and evaluation of a single value which will be known as a scalar product.

 The cross product of the vectors is another very important term that will help in resulting in the vector quantity and the dot product of the vectors is also considered to be a very important concept in this particular area.

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Basic points which justify the application of vectors in normal life:

  • The direction in which force has to be applied to moving a particular object
  • Understanding how gravity works
  • The motion of a body
  • Determination of the force applied on a body
  • Utilisation in the world of engineering
  • In different fields of oscillators
  • In application of quantum mechanics
  • Velocity into the pipe
  • General relativity and several other kinds of things

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