Why do we use $ijk$ for vectors?

Hint: Here in this question, we have been asked the reason behind the usage of $ijk$ for vectors. From the basic concepts of vectors, we know that $i,j,k$ are the unit vectors along the x-axis , y-axis and z-axis respectively. In the Cartesian coordinate system, any vector is generally represented in terms of its unit vectors.

Complete step by step solution:
Now considering the question, we have been asked the reason behind the usage of $ijk$ for vectors.
 From the basic concepts of vectors, we know that $i,j,k$ are the unit vectors along the x-axis, y-axis and z-axis respectively.
In the Cartesian coordinate system, any vector is generally represented in terms of its unit vectors.
Here unit vectors represent the direction of a vector.
We know that the vector is a physical quantity having both magnitude and direction.
The Cartesian coordinate system is used to represent a vector in three dimensions.
Generally any vector $\vec{P}$ in the Cartesian coordinate system is represented as $x\hat{i}+y\hat{j}+z\hat{k}$ .
The magnitude of the vector $P$ is represented as $\left| {\vec{P}} \right|$ and it is given as $\sqrt{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}$ .
Generally the magnitude of any unit vector is always one. This is why the name unit vector is coined for them. Unit vector is also known as a direction vector.

Note: While answering questions of this type, we have been asked to discuss the whole concept therefore our concept should be clear. Any vector can be represented in space using unit vectors. A unit vector lying along the direction of $\vec{P}$ is given as $\hat{p}=\dfrac{{\vec{P}}}{\left| {\vec{P}} \right|}$ .