Vectors have a magnitude and a direction. It can be pictured as a directed line, whose length is the magnitude of the vector. The arrow indicates the direction. The direction of the vector is from its tail to its head.
Vectors can be added by joining them head-to-tail.
Vectors can be subtracted by reversing the direction of the vectors.
The dot product of two vectors is the magnitude of one times the projection of the second onto the first.