Types Of Vectors, Definition, Properties & Importance - Maths

Types of Vectors

Scalars and Vectors are two rudimentary concepts in maths and physics. They define the type of quality of any physical or mathematical object. A scalar quantity is the one that contains only a magnitude value, whereas a vector quantity is the one that contains a magnitude as well as a direction. Let us imagine vectors as a line, the measurement of the line is the magnitude, and the arrow on this line is the direction in which it is travelling. The classic example of a vector quantity is force. The force has a magnitude with a direction in which the force acts. In mathematics, a total of 11 different types of vectors are studied. They are:

• 1. Zero vector
• 2. Unit Vector
• 3. Position Vector
• 4. Co-initial Vector
• 5. Like
• 6. Unlike Vectors
• 7. Co-planar Vector
• 8. Collinear Vector
• 9. Equal Vector
• 10. Displacement Vector
• 11. Negative Vector

A detailed description of all the types are given below:

Zero Vector or Null Vector

When the starting point and the finish point of a vector coincide with each other, it is known as a zero vector or null vector. The magnitude of such vectors is zero, and they, in particular, do not represent any direction.

Unit Vector

Vectors having a value of exactly one are known as a unit vector. Unit vectors are very important, and note that if two vectors are unit vectors, they are not specifically equal. They might have the same magnitude but can differ in their direction.

Position Vector

Position vectors are known to determine the position of any vector. A position vector is nothing but a point on any vector which tells the position of that vector in a plane

Co-initial Vectors

Vectors are expressed as co-initial vectors if they have the same origin point. This implies that the point of origin is common for these types of vectors, and then they may scatter in different directions. For example, let us consider two vectors PQ and PR; they are called co- initial vectors due to the fact they have the same beginning point, i.e., P.

Like Vectors

When two or more vectors share the same direction, they are known as like vectors.

Unlike Vectors

When two or more vectors travel in different directions, they are termed as unlike vectors.

Coplanar Vectors

Coplanar vectors are vectors (three or more) that lie in the same plane.

Collinear Vectors

These are also referred to as parallel vectors because they lie in the parallel line concerning their magnitude and direction.

Equal Vectors

Vectors having the same magnitude and the same directions are known as equal vectors.

Displacement Vector

The vector KL represents a displacement vector if a point is moved (displaced) from the position K to L.

Negative of a Vector

Let us assume that vector K has a magnitude ‘p’ and is in a certain direction, now let us suppose that another vector L is present having the same magnitude ‘p’ but travels in exactly the opposite direction of K. Thus, L is referred to as the negative of a vector K. K = -L Therefore, the negative of any vector is another vector with the same magnitude but opposite in direction.