Air traffic controllers give instructions called “vectors” to tell airline pilots in which direction they are to fly. If these are the only instructions given, is the name “vector” used correctly? Why or why not?

We need to understand what a vector and a scalar quantity are,

A vector is a way of expressing a quantity has both magnitude and direction.

A quantity defined by the magnitude as well as the magnitude's direction of action. For instance, consider the concepts of force and displacement.

Scalar quantity: Quantity that can be fully comprehended using only the magnitude value. Mass, temperature, and time are examples of scalar quantities.

A vector quantity consists of magnitude and direction, but as stated in the problem, the instruction given by the airline controller contained only direction. Since the magnitude is missing, it can not be a real vector quantity.

So the name ‘vector’ is misleading here.

So instand of giving the direction the pilot also have to give the magnitude of the vector, that is how much to north or at what degree to south.