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Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
In short, yes.
The length of the arrow signifies the magnitude or size of the vector.
A vector is represented graphically as an arrow. The direction indicates the direction, the length is proportional to the magnitude of the vector. Note that it is difficult to accurately represent vectors of 3 or more dimensions on a 2-dimensional sheet of paper.
A vector always consists of a direction and magnitude. For example, a vector representing the weight of an object that is 35N would be represented as an arrow pointing downward with a magnitude of 35N. You could also represent the weight of 35N as -35N, in which the negative symbol indicates a downward force.