Vector is a quantity with both a magnitude and a direction. In textbooks, vectors are denoted by a BOLD letter such as v. As it is hard to write bold letters in pen or paper, written work often uses different notation such as v, v, arrow or AB(arrow). The order of letters and arrows in the last example is important - in this case it tells us that the vector is going from point A to point B.
Column notation (column vectors) and horizontal bracket notation (row vectors) can be used to express vectors. Horizontal bracket notation has no commas between the components, and should not be confused with coordinates.
To obtain the vector expression/equation, assume that the starting point of the vector is placed at the origins of an axes with labels i, j, k (you may consider them to be equivalent to x y and z axes). The vector equation is then given by how far along the vector goes with respect to these axes.
Unit vectors are vectors that have a magnitude of 1, no matter the direction. Often, they are used to denote axes. A unit vector can be obtained by dividing a given vector by its magnitude.
Equal vectors are vectors which have the same magnitude and direction, regardless of where they are located. Say we have a vector r, then the negative vector −r has the same magnitude as r, but points in the opposite direction.