Types of Vectors: Definition, Properties & Examples

Vector is defined as a physical quantity that has both magnitude as well as direction. Vector describes the movement of an object from one point to the other as well as its direction. The starting point of the vector is known as the tail and the endpoint of the vector is called the head of the vector. There are 10 different types of vectors, namely,

1. Unit Vector
2. Co-Initial Vector
3. Coplanar Vector
4. Equal Vector
5. Negative of a Vector
6. Zero Vector
7. Position Vector
8. Like and Unlike Vectors
9. Collinear Vector
10. Displacement Vector

Read More: Determinant Formula

Key Terms: Types of Vectors, Coplanar Vector, Co-Initial Vectors, Terminal Point, Collinear vectors, Zero Vectors, Like and Unlike Vectors

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Unit Vector

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A vector is called a Unit Vector when it has a magnitude of 1 unit length. For example, if a (vector) has a magnitude of a then its unit vector will be denoted by a(cap), and its direction will be a(vector) having magnitude 1.

The video below explains this:

Types of Vectors Detailed Video Explanation:

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Co-Initial Vector

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Two or more vectors that have the same initial point are known as Co-Initial Vectors. For example, XY and XZ are Co-Initial vectors that have the same initial point ‘X’.

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Coplanar Vector

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Vectors that lie either in the same plane or which are parallel to the same plane are called Coplanar vectors. If the vectors are in same direction then they ae called Concurrent Vector and if the vectors are in different directions then they are called Non-Concurrent vectors.

Read More: Co Planar Vectors

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Equal Vector

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When two vectors have equal direction as well as magnitude, they are known as Equal Vectors, even if the initial point is different for both the vectors. If there are two vectors A and B having the same directions and magnitude irrespective of their initial point, then these vectors will be called Equal Vectors and will be written as,

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Negative of a Vector

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When two vectors have the same magnitude but they both have exactly different directions. For example, A and B are two vectors having the same magnitude but a different direction, then it can be written as:

A = -B

Read More: Negative of a Vector

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Zero Vector

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A vector is known as a Zero vector when its starting and ending point is the same and it has zero magnitude. The starting point needs to coincide with the terminal point. For XY, the coordinates of both X and Y are the same. Thus it is called a Zero vector and will be denoted by 0. The direction of a zero vector is indeterminate. Zero vector is also known as null vector.

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Position Vector

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A vector that denotes the location or the position of a point in a plane (three-dimensional Cartesian system) with respect to its origin. If A is a reference origin and there’s an arbitrary point B in the plane then AB will be known as the position vector of the point.

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Like and Unlike Vectors

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Vectors that have the same direction are known as Like Vectors. And when the vectors have opposite directions to each other then they are called Unlike Vectors.

Read more: Rolle’s Theorem

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Collinear Vector

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Vectors that are lying either in the same line or which are parallel to the same line are called Collinear vectors. They can be in the same direction or they can be in the different directions. These types of vectors are also known as Parallel Vectors.

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Displacement Vector

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The vector AB will be known as a displacement vector if a point is displaced from the position B to position A. In the diagram given below, the position vector of the particle at point A is OA and when it is at point B, the position vector is OB. The displacement vector in this case is the vector joining the initial position to its final position.

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Things to Remember

• Vector is defined as a physical quantity that has both magnitude and direction.
• There are 10 types of vectors.
• When the magnitude is 1, it is called a unit vector.
• If two vectors start from the same point, it is called Co-initial vectors.
• If two vectors lie in the same plane, it is called Co-planar vectors.
• If two vectors have equal magnitude and travel in the same direction, it is called equal vectors.
• If two vectors have same magnitude but opposite direction, it is called negative vectors.
• If the starting and ending position of a vector is the same, it is called zero vector.
• If a vector denotes its position in a three dimensional system, it is called position vector.
• If two vectors have same direction it is called like vectors and if it is in opposite direction, it is called unlike vectors.
• If two vectors lie in same line or are parallel to each other, it is called collinear vectors.
• If the position of a vector is displaced from one point to another, it is called displacement vector.

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Previous Years’ Questions

1. If a and b are vectors such that |a+b|=|a−b||a+b|=|a−b| then the angle between a and b is [KCET 2007]
2. If →aa→ and →bb→ are unit vectors and |→a+→b|=1|a→+b→|=1 then |→a−→b||a→−b→| is equal to? [KCET 2008]
3. If a and b are vectors such that |a+b|=|a−b||a+b|=|a−b| then the angle between a and b is? [KCET 2007]
4. OA and BO are two vectors of magnitudes 5 and 6 respectively… [KCET 2007]
5. If →a,→ba→,b→ and →cc→ are unit vectors such that… [KCET 2011]