There are many forms of vector notation.  If you pursue a degree in physics, you might learn several different notations.  For the moment, we’ll introduce a simple notation, and then expand on it later.

Vector Notation

As mentioned earlier, you can represent a vector by picking a convenient letter, like for a displacement vector, and place a small arrow above it, resulting in \(\color{black}{\vec{d}}\).  You will often have several vectors of the same type, so you might give each a subscript, for example, \(\color{black}{\vec{d}_1}\), \(\color{black}{\vec{d}_2}\), and \(\color{black}{\vec{d}_3}\).

Vectors in older textbooks or websites might be represented by bold letters, so \(\color{black}{\vec{d}_1}\) could be written as d_1 or \(\color{black}{d_1}\).

As modern word processors and websites allow easier representation of arrows and subscripts, you will likely not see this notation as often.  The exception is in e-mails from your professor.  The _1 is used to represent a subscript of 1.

Backwards Vector Arrows

A few professors might suggest that you use a backwards arrow to represent a vector pointing in the opposite direction.  If vector \(\color{black}{{d_2}}\) points opposite to \(\color{black}{{d_1}}\), you might write them as \(\color{black}{\vec{d}_1}\) and \(\color{black}{\overleftarrow{d}_2}\).

I personally dislike this notation.  If vectors point up or down, for example I would never represent them with vector symbols pointing up or down over my variable.

Magnitude

You can think of magnitude as a generic term for length.  For example, it does make sense to say a displacement vector has a length of 2.3 meters.  A velocity vector, however, has a “length” that is not measured m/s, which are not in dimensions of length.

Using the term magnitude allows us to convey the idea of length without requiring us to use length units.

To represent the magnitude of a vector \({\vec{d}}\), there are three ways to write the magnitude.

d is the simplest.  Just write the letter representing the vector.

\({|\vec{d}|}\) also works.  Think of this as an absolute value sign, removing the direction.

\({||\vec{d}||}\) works as well.

My personal preference is to just write the letter, I do this because it I treat the magnitude of the vector as a variable in my equations.  Realize that you will see all three notations, depending on your textbook, online resource, and professor.  Make sure to use the notation your professor prefers.