Equality of Vectors

What are vectors?

Recall that a vector is a mathematical quantity that has both magnitudes and directions. The length of a line can be described as its magnitude, while the arrow represents its direction. Its tail is the start point, and its head is the endpoint. When it comes to vectors, the best illustration is temperature change, which increases and decreases in both direction and magnitude. There are 10 types of vectors We will discuss different types of vectors. There are 10 types of vectors that are often used in maths. These are the 10 types of vectors:

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

Let’s discuss them in detail

Null Vector or Zero Vector

A vector is a Zero Vector if its magnitude is zero and its starting point and endpoint are the same. For example, RS can be a line segment whose coordinates, point R are the same as those of the point S. A zero vector is indicated by 0. The zero vector does not have a definite direction to point in any particular direction.

Unit Vector

This is represented by a lowercase letter with a cap (‘^’) symbol. A vector is considered a unit vector if its magnitude is 1 unit. Let’s say that y is a unit vector, in which case, it will be written as y. The formula for a unit vector is as below: unit vector=vectormagnitude of the vector Two unit vectors can’t be the same, as they may have different directions.

Position Vector

Here, the position vector of point A representing the position of point A in accordance with the fixed point O is vector OA. Say x, y, z are coordinates of the said point A, then OA=x_i+y_j+z_k.  

Co-initial vectors

Co-initial vectors are when more than one vector has the same starting place. For example, vectors OA and OB are co-initial because they both have the same starting position O.

Like and Unlike Vectors

Vectors with the same direction are called like vectors, while vectors with opposite directions are called unlike vectors.

Coplanar Vectors

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

Collinear Vectors

Collinear vectors are vectors that lie in parallel lines or along the same line in respect to their magnitude or direction. They are also known as parallel vectors.

Equal Vectors

Two vectors can be considered equal if they both have the same direction and magnitude, even though they may have different starting points.

Displacement Vector

If a point is moved from P to Q, the vector PQ will represent a displacement vector.

Negative of a vector

Let’s say that a vector has the same magnitude as a direction. Now, if a vector with the opposite magnitude is given, this vector will be called negative of a vector. Consider two vectors, p and q. If they are equal in magnitude but have opposite directions, then the vectors can be described as p= -q.