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.
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:
Like and Unlike Vectors
Negative of a Vector
Let Us Discuss Them in Detail
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.
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.
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
What is the collinear vector?
Two vectors say a and b are given then they are said to be collinear vectors if they are parallel to each other. They can have different magnitudes or equal magnitude and their direction can be the same or even opposite.
Let us get more familiar to collinear vectors with an example:
Suppose we have a vector given
Then the collinear vectors are:
From the above picture it is clear that all three vectors have different magnitude and different directions but they are parallel to each other so we can say that all the three vectors are collinear vectors.
What is the zero vector?
The zero vector is a vector with its magnitude as 0. It is also known as the null vector. Consider this figure, where the vector O covers 0 magnitude means its starting point and the initial point is the same then it is said to be a zero vector or null vector. The dimension of zero vector are always zero i.e. O(0,0) in two dimensional, O(0,0,0) in three dimensional and so on.
For example, A person traveling from a point 1 km to north direction and returns back 1 km in the south direction to the same point. Here we can see that the magnitude is 2km but the starting point and the endpoint are the same so the magnitude is zero and said to be null so it is said to be zero vector.