Types of Vectors: Overview, Questions, Preparation

Vector Algebra 2021 ( Vector Algebra )

Rachit Kumar Saxena

Rachit Kumar SaxenaManager-Editorial

Updated on Jun 29, 2021 11:17 IST

What are the types of Vector?

In mathematics, a quantity that has both direction and magnitude is a vector. Vector has its importance in each field like in determining position, the direction of an object, etc. 

There are in total, ten types of vectors present. They are defined below:

1. Unit Vector: A vector is a unit vector if its magnitude is 1. It is written with the ‘^’ "hat" symbol. 

2. Like and Unlike Vectors: When the vectors' directions are opposite with respect to each other, they are known as Unlike Vectors. When their directions are the same, they are known as Like Vectors.

Types of Vector

3.Equal Vector: An equal vector has the same direction and magnitudes.

Types of Vector

4. Negative Vector: When the magnitude of the two vectors are equal, but their directions are opposite, then they are negative vectors of each other.

Types of Vector

5. Zero Vector: A vector whose magnitude and components are zero is a Zero Vector. It is represented by 0 or with (→) on 0. 

6. Position Vector: Position vector denotes a point's position or location in the three-dimensional Cartesian system with respect to a reference origin. It is represented by ( rˆ ).

7. Co-initial Vector: Suppose we have two vectors and both have the same starting point then they will be termed as Co-initial Vectors.

Types of Vector

8. Co-planar Vector: When three vectors or more than that lie in the same plane or parallel to the same plane, they are termed co-planar vectors.

Types of Vector

9. Collinear Vector: When the vectors lie on parallel lines or the same line, they are called collinear vectors.

Types of Vector

10. Displacement Vector: A displacement vector represents the shortest distance when a point is shifted from one place to another.

Weightage of Topic

Types of Vectors is present in class XII mathematics chapter Vector Algebra. The chapter's applications also have its importance in other subjects like physics. In class XII mathematics exams the weightage of vector algebra along with three-dimensional geometry ranges from 12 to 14 marks. 

The chapter of Vector Algebra also includes topics such as:

  • Operations of Vectors(Addition, Subtraction)
  • A Scalar multiplication with a Vector
  • 2 Vectors' Product

Illustrative Examples on Types of Vectors

1. From the given figure, identify which vectors are Collinear, Coinitial, and Equal Vectors.

Types of Vector

Solution.

Types of Vector

2. If the given vectors Types of Vector  are equal vectors then evaluate the values of a, b, and c.

Solution.

If the 2 given vectors are equal then 

a = 2, 

b = 2, 

and c = 1.

3.

Types of Vector10

FAQs on Types of Vector

Q: If a vector's magnitude is zero, then what will be its direction?

A: For zero vectors the directions are indeterminate. 

Q: What is the other name of Collinear Vectors?

A: Parallel Vectors

Q: Which among the two is a scalar quantity and which one is a vector quantity?

 A: 
Distance
Speed
Density
Velocity

Q: What is the formula to find the unit vector of x?

A: x = x|x|.

Q: Mention one real-life use of Vectors?

A: Vectors can be used in determining the direction of a falling object.

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