Do all vectors must have a "Direction " and "Magnitude"? Pleases explain it as easy as possible,I started to learn linear algebra of vector a few week ago.If it so ,then the next question is that if I take an element(indeed a vector) of "any" vector space ,then how can I find its particular "magnitude" and "direction"?
 A: In short, no.  When you are just starting to study linear algebra, all of the vector spaces you will see for a while are finite-dimensional vector spaces where the scalar field is the real numbers, and in these vector spaces, both magnitude and direction make sense.  Every vector in these vector spaces has a magnitude, and almost every vector has a direction.  But there is one exception:  the zero vector has zero magnitude but does not have any definable direction.
More generally (and you should start seeing some of these more general examples pretty soon in your studies), the answer to your question depends on what you mean by a "vector."  In order for a vector to have a magnitude, the vector space must support a norm, and not all vector spaces do; similarly, in order for a vector to have a direction, the vector space must support an inner product, and not all vector spaces do.  An inner product can be used to define a norm, though, so if a vector field suports having directions for its vectors, then it supports magnitudes, too.
Getting back to finite-dimensional vector spaces where the scalar field is the real numbers, these spaces support both a norm and an inner product, so magnitude and direction both make sense.  Except for the zero vector, as above.
