Types Of Vectors - Practice Questions & MCQ

Zero or Null Vector

A vector whose initial and terminal points coincide, is called a zero vector (or null vector) and it is denoted as $\overrightarrow{0}$. The magnitude of zero vector is zero and the direction of zero vector is indeterminate.

It can also be denoted by $\overrightarrow{A A}$ or $\overrightarrow{B B}$ etc.
Unit Vector
A vector whose magnitude is unity (i.e., 1 unit) is called a unit vector.
The unit vector in the direction of a given vector $\vec{a}$ is denoted by $\widehat{\mathbf{a}}$ read as "a cap". Thus, $|\widehat{\mathbf{a}}|=1$.

$
\hat{\mathbf{a}}=\frac{\overrightarrow{\mathbf{a}}}{|\overrightarrow{\mathbf{a}}|_{\mid}}
$

Coinitial Vectors

Two or more vectors having the same initial point are called coinitial vectors.

Collinear/Parallel Vectors 

Two or more vectors are said to be collinear (or Parallel) if they are parallel to the same line, irrespective of their magnitudes and directions

Like and Unlike Vectors

Vectors are said to be like when they have the same direction and unlike when they have opposite directions.

Both like and unlike vectors are parallel to each other.

Equal Vectors

Two vectors $\vec{a}$ and $\vec{b}$ are said to be equal, if they have the equal magnitude and same direction regardless of the positions of their initial points, and written as $\vec{a}=\vec{b}$.

Negative of a Vector
The vector which has the same magnitude as that of a given vector (say $\overrightarrow{\mathbf{a}}$ ) but having opposite direction.
It is denoted by $-\overrightarrow{\mathbf{a}}$.
Thus if $\overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{A B}}$ then, $-\overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{B A}}$

Coplanar Vector

A system of vector is said to coplanar if they lie on the same plane.

Note: 2 vectors are always coplanar.