Question

What units are associated with unit vectors i , j and k

Answer 1

First of all, not to get confused with terminology, unit vectors are called unit vectors because they have a unit length. This has absolutely nothing to do with physical units.

Now, if you are talking about physical units like m, m/s or N. Then it depends on what physical vector quantity you’re talking about. If it’s the displacement vector then the i,j,k will have units of length i.e. meters (m). If it’s the force vector then the i,j,k will have units of force i.e. newtons (N).

But if you are talking about vectors in math, then they are unitless. So, we just pretend the physical unit is 1.

Again stressing that this has nothing to do with their name “unit vectors”. They are called that because the unit, AKA the number “1”, is the value of their magnitude/length.

They have magnitude 1, bearing the unit of physical quantity they represent.