What are Vectors?
To recall, in Mathematics a physical quantity that has both magnitude and a direction is said to be a vector. In a line, the length of a line is a magnitude and the arrow is its direction. The start point is its tail and the endpoint is its head.
An increase and decrease in temperature is the best example of a vector, it has both magnitude and direction.
10 Types of Vectors
Here we will be discussing different types of vectors. There are commonly 10 different types of vectors frequently used in maths. The 10 types of vectors which are:
- Zero vector
- Unit Vector
- Position Vector
- Co-initial Vector
- Like and Unlike Vectors
- Co-planar Vector
- Collinear Vector
- Equal Vector
- Displacement Vector
- Negative of a Vector
Let Us Discuss Them in Detail
Zero Vector or Null Vector
A vector is said to be a Zero Vector when the magnitude of the vector is zero and the starting point and the endpoint of the vector is the same. For instance, PQ is a line segment the coordinates of the point P are the same as that of the point Q. A Zero vector is denoted by 0. The zero vector doesn’t have any specific direction.
A vector is said to be a unit vector when the magnitude of the vector is of 1 unit in length. Suppose if x is a vector having a magnitude x then the unit vector is denoted by x̂ in the direction of the vector and it has the magnitude equal to 1.
But two unit vectors cannot be equal as they might have different directions.
Any point X taken in the plane is said to be a position vector. It simply denotes the position. Let OX a point in a plane with respect to its origin.
Let us consider O is taken as reference origin and X is an arbitrary point in the plane then the vector is called the position vector of the point.
A vector is said to be co-initial vectors when two or more vectors have the same starting point, for example, Vectors AB and AC are called co-initial vectors because they have the same starting point A.
Like and Unlike Vectors
The vectors having the same directions are said to be like vectors whereas vectors having opposite directions are said to be unlike vectors.
Three or more vectors lying in the same plane are known as coplanar vectors.
Vectors which lie in the parallel line or in the same line with respect to their magnitude and direction are known to be collinear vectors, also known as parallel vectors.
Two vectors are said to be equal vectors when they have both direction and magnitude equal, even if they have different initial points.
The vector AB represents a displacement vector if a point is displaced from the position A to B.
Negative of a Vector
Suppose a vector is given with the same magnitude and direction, now if any vector with the same magnitude but the opposite direction is given then this vector is said to be negative of that vector.
Consider two vectors a and b, such that they have the same magnitude but opposite in direction then these vectors can be written as
a = – b
Let Us See Some Examples to Understand the Types of Vectors.
Identify the vectors
Vectors a and c are unit vectors because they have magnitude 1.
Vector a and c are equal vectors because they have the same magnitude and same direction
Vectors b, c and d have the same initial point so they are co-initial vectors.
Let us take the points P(1, 0, 0), Q(0, 1, 0) and R(0, 0, 1) on the x-axis, y-axis and z-axis, respectively. Identify the vectors.
OP =1; OQ =1; 0R =1;
Therefore, the vectors OP, OQ and OR, are called unit vectors.
Identify the vectors