Question

Why do we use $ijk$ for vectors?

Answer 1

Explanation:

1. $i,j,k$ are the unit vectors in the directions $x,y,z$ respectively.
2. Vectors in general have both magnitude and direction, they use some linear combination of $i,j,k$ to represent a particular vector which contains the information of both direction and magnitude of the vector.
3. let's say $\overrightarrow{P}$ to be a vector then it is represented as $\overrightarrow{P}=x\hat{i}+y\hat{j}+z\hat{k}$ where the magnitude is $\sqrt{x^2+y^2+z^2}$.
4. If they ask why specifically $i,j,k$, It's just convention to represent unit vectors that are accepted worldwide.

Hence, we use $ijk$ for vectors.