# Zero vector or null vector

A vector whose initial and terminal points are coincident is called the zero vector or the null vector. The magnitude of the zero vector is zero and it can have any arbitrary direction and any line as its line of support.

# Unit vector

A vector of unit magnitude is called a unit vector. Unit vectors are denoted by small letters with a cap on them. If the vector is divided by magnitude , then we get a unit vector in the direction of .

# Like and unlike vectors

Two parallel vectors having the same direction are called like vectors.

Two parallel vectors having opposite directions are called

**unlike vectors.**# Collinear vectors

Vectors which are parallel to the same vector and have either initial or terminal point in common are called collinear vectors. If vectors and are collinear then , where

*λ*is scalar. Collinear vectors are called dependent vectors.

*Notes:*- Two non-zero vectors and are collinear iff there exists scalars
*x*,*y*not both zero such that - If are any two non-zero non-collinear vectors and
*x*,*y*are scalars, then = 0 ⇒*x*=*y*= 0. **Collinearity of points:**Let*A*,*B*,*C*be three collinear points. Then, each pair of the vector , is a pair of collinear vectors. Thus to check collinearity of three points, we can check the collinearity of any two vectors obtained with the help of three points.- Three points with position vectors, and are collinear if and only if there exists three scalars
*x*,*y*,*z*not all simultaneously zero such that together with*x*+*y*+*z*= 0.

# Non-collinear vectors

Two vectors acting in different directions are non-collinear vectors.

Non-collinear vectors are called independent vectors.

# Free vectors

Vectors whose initial point is not specified are called free vectors.

# Equal vectors

Two vectors are said to be equal, if they have the same magnitude and same direction.

# Coplanar vectors

Vectors are said to be coplanar if all of them lie in the same plane. Three coplanar vectors are always dependent.

If vectors , and are coplanar then there exists scalars

*λ*and*μ*such that .or = 0

where

*a*,_{i}*b*,_{i}*c*(_{i}*I*= 1, 2, 3) are components of vectors , and in the direction of*x*,*y,*and*z*axis.Four points with position vectors are coplanar if with

*λ*_{1}+*λ*_{2}+*λ*_{3}+*λ*_{4}= 0.# Position vector of a point

If a point

*O*is fixed in a space as origin then for any point*P*, the vector is called the position vector (PV) of “*P*” w.r.t. “*O*”.Also = =

*PV*of*B*–*PV*of*A.*