Vectors
We’re demystifying the symphony of vectors, its notation, transforming confusing symbols into your new allies. Dive into our step-by-step guide to vector calculations, unraveling the complexity and making equations a breeze.
Douglas Tawiah Dwumor
- A vector has both magnitude and direction
- Vectors can be represented using either uppercase or lowercase letters.
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A vector is a quantity which has both magnitude and direction. Examples of vector quantities include force, displacement, velocity, acceleration, electromagnetic field, momentum, torque, etc
Note: Force is a push or pull. This push or pull occurs in a specified direction. Hence, force is a vector quantity.
A quantity which has only magnitude but no direction is called a scalar quantity. Examples of scalar quantities include mass, distance, speed, pressure etc. Note: The mass of a body is the quantity of substance in the body. This quantity has no specified direction. The quantity of substance is contained in the body and it stays put without any direction.
Vector Notation
A notation is a written symbol that is used to represent something. Vectors are typed or written with special symbols to differentiate them from scalar quantities. We write vectors using two uppercase letters with an arrow on top of the letters to show the direction of the vector.
Example : 
is read as “vector AB”. Note that the arrow on top of the two letters AB means the direction of the vector is from A to B. In the same vein, 
means the vector is from B to A.
Vectors can also be represented using a lowercase letter. Such vectors are called position vectors. A position vector is a vector that represents the position of a point in space relative to a reference point, often the origin of a coordinate system.
Position vectors are represented using lowercase letter in boldface if it’s typed.
Example, 
, 
, 
etc
If the position vector is written with free hand, it is underlined or a scribble is put beneath it to show that it’s a vector. Example, 
Alternatively, an arrow can be put on the lowercase letter. For example 
.
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