Question

What is $\widehat{i}$ and $\widehat{j}$ in a vector?

Answer 1

In this type of question we may try to find the definition of vectors, try to know about coordinate axes, we may draw different vectors in a graph and try to do some problems related to vectors and imagination is a very necessary point here to know conceptually about this question.

Complete step by step answer:
The quantity which has both magnitude and direction is known as a vector. It is represented with the help of a straight line with an arrow head. This length of the straight line denotes the magnitude of the vector and the arrowhead shows the direction of the vector. Vectors are represented as $\overrightarrow{A}$.
A vector has mainly two components such as horizontal component and vertical component. Arithmetic operations such as addition, subtraction and multiplication can be performed on vectors but we cannot do the division of two vectors, it’s not possible.
Types of vectors are as:
Zero Vector – This can be defined as the vector which has $0$ magnitude.
Unit Vector – It can be defined as the vector of unit $1$.
Position Vector – A vector which is used to denote the position of a point with respect to its origin.
Co-initial Vector – Two or more vectors that have the same starting or initial point known as co-initial vector.
Like and unlike vectors – The vectors that have the same direction known as like vectors and the vectors that have different directions known as unlike vectors.
Coplanar Vector – The vectors that are in the same plane known as coplanar vectors.
Collinear Vector – The vectors that lie on the same straight line known as collinear vectors.
Equal vector – Two or more vectors that have the same magnitude and direction are equal vectors.
Displacement Vector – These vectors are used to indicate the displacement of an object from one point to another.
Negative of a Vector – Negative of any vector can be defined as the vector which has the same magnitude but opposite direction.
$\widehat{i}$and $\widehat{j}$ in a vector are unit vectors along the $X$ and $Y$ axis respectively. $\widehat{i}$ and $\widehat{j}$ are commonly used to denote the perpendicular unit vectors in $2d$ plane. Any point in a $2d$ plane can be specified by using these two unit vectors.
Hence this is all about $\widehat{i}$ and $\widehat{j}$ in vectors.

Note: Most commonly in physics, vectors are used to represent displacement, velocity, and acceleration. Vectors are a combination of magnitude and direction, and are drawn as arrows. The length represents the magnitude and the direction of that quantity is the direction in which the vector is pointing.