Physical quantities are divided into two categories:

**Scalars quantities:**They have only the magnitude. For example, mass, length, time, temperature etc. The scalars quantities can be added, subtracted, multiplied and divided just as the ordinary numbers.**Vectors quantities:**They have both magnitude and direction. for example velocity, force, electric field, torque etc.

A vector can be defined as a line segment having a specific direction and a specific length. The length is the magnitude of the vector and with an arrow indicating the direction. The direction is from the tail of the vector to its head.

*Figure:5.a*

A vector is denoted by the letter in bold (for example vector p is written as **p**) or it can be represented by an arrow placed over a letter (for example vector is written as

*Position and displacement vectors:*

A position vector describes the position of a point in a coordinate system.

*Figure:5.b*

If P is the position of an object at time t, then OP is the position vector of the object at that time. It is denoted by

The displacement vector describes the position of a point with reference to a point other than the origin of the coordinate system.

*Figure:5.c*

An object moves from a point P to point Q. Let

**Parallel vectors and antiparallel vectors:**

Parallel vectors act along the same direction and they are collinear. The angle between them is $0^{0}$.

*Figure:5.d*

Antiparallel vectors act in the opposite direction and they are collinear. The angle between them is $180^{0}.$

*Figure:5.e*

**Equality of vectors:**

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

*Figure:5.f*

**Unit vector:**

Unit vector has a unit magnitude and points in a particular direction. Any vector

can be written as the product of unit vector in that direction and magnitude of the given vector.

Unit vector is expressed as

We can write,

A unit vector has no dimensions. Unit vectors along the positive X, Y and Z -axes of the coordinate system can be expressed as

*Figure:5.g*