A vector is represented graphically by a directed line segment or an arrow head line segment.The length of line,according to the scale chosen ,represents the magnitude of the vector while arrow head indicates the direction.Also they follow triangle law of addition.For example force,acceleration,torque,momentum ,angular momentum etc.To represent a vector we need:
- A suitable scale
Reference axis x,y & z axis ,vertical and horizontal directions or the directions of east and west,north and south.
Types of vectors
In general vectors may be divided into three types.
- Proper vectors
- Axial vectors
- Inertial or pseudo vectors
Displacement ,force,momentum etc are the proper vectors.
The vectors which act along the axis of rotation are called axial vectors.For example ,angular velocity,torque,angular momentum,angular acceleration are axial vectors.
Pseudo or inertial vectors
The vectors used to make an inertial frame of reference into inertial frame of reference are called pseudo or inertial vectors.Vector may be further divided as:
A unit vector is that whose magnitude is unity i.e 1 and has any given direction only.A unit vector is obtained by dividing the vector with magnitude.
A vector which can be displaced parallel ti itself and applied at any point is called a free vector.
A vector that represents the position of a point with reference to a fixed point is called position vector
A vector having the same magnitude as that of given vector but opposite direction is called negative vector.
- A vector whose magnitude is zero and has no direction,it may have all directions is said to be a null vector.A null vector can be obtained by adding two or more vectors.
Like or parallel vectors
If two vectors have the same direction but different magnitude are called parallel or like vectors.
Two vectors having opposite directions and unequal magnitudes are called unlike vectors.
Two vectors are said to be equal if they have equal magnitudes.
Co -initial vectors
If vectors have a common initial point,then these types of vectors are called co initial vectors.
Vectors are called co-linear if they have in same line or parallel.
- Vectors which are lying in same plane are called co- planar vectors.