Vector is the wide subject used in math and physic. Vector calculator is related with addition, subtraction, unit, cross product etc.. A vector is a mathematical object that has magnitude and direction.
The vector is the direct line segment with showing direction upwards. A line of given length and pointing along a given direction is the typical representation of a vector. The 2 ending points is described as Initial and Terminal . Where S is the Initial and Q is Terminal, and it is denoted as $\vec{SQ} $.
Direct Line Seg
Types of Vectors:

Unit vectors: A unit vector is a vector with a magnitude of 1. It is denoted by symbol $\vec{a}$ where $\left | \vec{a} \right | = 1$

Like Vectors: Two vectors $\vec{a}$  and  $\vec{b}$ are like vectors only if they have the same direction. If they have the opposite directions they are said to be the unlike vectors.

Zero (Null) Vectors: The vector whose magnitude is zero means the initial and the terminal points are coincident are known as the Zero vector.

Proper Vectors: A vector which is not zero vector is called proper vector. Thus $\vec{a}$ is a proper if its modulus (magnitude) a is not zero   $\left | \vec{a} \right | \neq 0$.

Negative of a Vectors: A vector having the same magnitude as that of a given vector but directed to the opposite sense is called the negative vector. Negative vector is denoted by $ - \vec{a}.$

Example:  If  $\vec{SQ} = a$  and   $\vec{QS} = -a$
                 then $\vec{SQ} = -\vec{QS}$

Co-initial Vectors: The vectors which have the same initial point are called co-initial vectors.

Reciprocal Vectors: The two vectors which have the same direction but whose lenght are reciprocal of each other then it is said to be the reciprocal vectors.
If $\hat{a}$ denotes the unit vector in the direction of a vector $\vec{a}$ , then
               $\vec{a} = \left | \vec{a} \right | \hat{a},  and  \frac{1}{\vec{a}} = \frac{\hat{a}}{\left | \vec{a} \right |}$
Hence the vectors $\vec{a}$ and $\frac{1}{\vec{a}}$ are the reciprocal.

The reciprocal of a unit vector is the unit vector (self - reciprocal) itself.
Localised Vector: A vector which are restricted to pass through a given point are called localised vectors.

Free Vector: A vector is said to free or non-localised vector, if its origin can be taken anywhere is space.