Can we say that a scalar is a special case of vector? I am studying linear algebra and I have been having trouble with fully understanding the concept of vector. The definition from wordnik says 
A quantity, such as velocity, completely specified by a magnitude and a direction.
As I understand, any quantity is a vector or actually CAN be described with a vector. And a scalar is just a special case of a vector that is specified with one quantity. If we say, for example, SCALAR speed of a car A = 5, we can say that the vector speed of a car A = 5 * i + 0*j + ..., where i, j, ... are unit vectors.
So, my question is,
Why do we need the concept of scalar?
If one concept can describe every quantity, why give another name to a spacial case quantity?
 A: Simple: multiplication between vectors is not defined, but multiplication between scalars is. If you consider scalars to be a 1-D vector, then you have a weird situation where $\mathbf{a}\mathbf{x}$ is defined only if $\mathbf{a}\in \mathbb{R}^1$, but never when $\mathbf{a}\in \mathbb{R}^n$ for $n > 1$.
Arguably, you could also say that the definition of a vector is predicated on the existence of scalars, as the vector space axioms require scalar multiplication of vectors.
A: I was kind of with you up until $A = 5*\mathbf{i} + 0*\mathbf{j} + ...$ because there you've implicitly used more than one scalar (you're assigning 0 to all other directions).  Only in 1D will you have a vector that can be represented by precisely one scalar value, because it is enough to give both magnitude and direction (here the direction is based only on the sign of the scalar).  
In any higher dimension $n > 1$, you will need $n$ scalars to represent the direction of your vector, the special case arguably being a zero vector where all directions are in a sense equivalent when given zero magnitude. 
A: The temperature field (i.e. the assignment of temperature to each point in a space) is composed of magnitudes and not directions.  The idea of "direction of temperature" is just borked.
Additionally, vectors are inadequate.  Stress-strain relations require tensors (machines, like matrices, that take two vectors and reduce them to a scalar, or that takes a vector and reduces to another vector).  Vectors just aren't enough to describe everything that needs describing.
