Question 3: What units are associated with unit vectors, î, ĵ and k̂?
Unit vectors have no units. It just specifies the direction along a certain coordinate axis and therefore, has its importance in the vector representation. For example, consider a displacement of 5 cm along x-axis. This displacement is represented as.
A = 5cm î
Do not confuse with the use of the word ‘unit’. Unit has its dictionary meaning as 1 (one). Similarly, in Physics, unit is the specific amount of a quantity with which a certain amount of that quantity is measured. For example, 1 kg is a specific amount of mass. If we have a certain quantity of mass of sugar, we measure that quantity of sugar with kg to find the mass of sugar. Or 1 s is a specific amount of time with which we measure the time (a quantity) taken by some event to happen.
Here the unit ‘cm’ is part of the magnitude of the displacement and not the direction. The unit vector î tells us that the displacement is along the x-axis.