How do you define a vector?

Hint: Vectors are normally a scalar quantity given with direction, or we can say that vectors are normally magnitudes of any quantity that are given with directions. Vectors are shown with an arrow symbol above them but this arrow does not define their direction. Do not confuse that the arrow points towards the direction of the vector.

Complete answer:
Vectors are ordinary quantities that are given with direction, basically any magnitude which is given with a direction is a vector quantity. Any quantity that is defined without any direction are called scalar quantities. Vector quantities play an important role in physics. When we define a force, we always define in what direction the force is acting. Hence force is a vector quantity. Vectors are also used in our everyday life, for example when we say that some object is moving with a speed in this particular direction then this is a vector quantity because we are defining a direction with it. Vectors follow some rules like Law of vector addition and cross product etc. these laws work differently for both vector and scalar quantities. Vectors are used widely in both physics and mathematics and also play a major role in engineering.

Note:
Even though a vector is a quantity with direction, this does not define its position. Vector consists of only direction with magnitude and not the location coordinates. Do not confuse the direction of the vector with its location. Both are different things. Location can only be defined with time coordinates for a particular instant of time (In case of moving objects) while directions can be defined without time coordinates.