Vectors in the Plane

Vectors in the plane: The quantities which has magnitude as well as direction, such quantities are called Vectors.It can not be completely characterized by a single real number. To represent such quantity, we can use a line segment, which has some initial pointand the terminal point. Its magnitude is denoted by $\left \| \vec{PQ} \right \|$ can be found by the distance formula.

In the first diagram $\left \| \vec{PQ} \right \|$, P is the initial point and Q is the terminal point.
If two or more directed line segments that have the same magnitude and direction are equivalent. In the second diagram all the vectors are equivalent. The set of all directed line segments and that are equivalent to the line segment $\left \| \vec{PQ} \right \|$ is a vector v in the plane and it is written as v =$\left \| \vec{PQ} \right \|$. Vectors are denoted in lowercase but in bold letters such as u,v and w .

Real life example on vectors in the plane

1) In our daily life, we are using vectors unknowingly such as when we direct our friend to whom we invite at our place. Like turn left drive straight for 2 km etc.
2) Pilot receive instructions to land the airport. At that time, the air traffic control instructs pilots to fly in a particular direction for a particular distance which is nothing but the magnitude. So this is nothing but the vector quantity which has magnitude and direction.