User:Jdiwad/Vector (mathematics and physics)

Article: Vector

Give a general overview on what a vector is

Talk about their application in physics while touching on them in mathematics

Describe difference between a vector and a scalar.

Showcase the different types of notation for writing a vector

Explain how vector addition and subtraction works graphically and "written"

Show examples of topics in physics that involve vectors (like velocity, momentum, etc..)

Vectors in Physics
A vector in physics is a measurement that has a direction and magnitude. Vectors are commonly represented graphically by an arrow-headed line but are equally shown through notation. Vectors are not locked to describing only one unit and are describe a lot of different quantities in science.

Applications of Vectors
In physics, many quantities are expressed as vectors including velocity, acceleration, displacement, and others. As previously noted vectors have a direction and magnitude and that is seen in its components. A vector component contains information about direction and magnitude in each axis that is relevant and with those components there are operations like dot product, cross product, or vector addition that allows for manipulation of said components and vectors as a whole.

Scalars
From the overview, vectors are objects that have a direction and magnitude but scalars are vectors with the exception of direction. Examples of scalars are speed, time, mass, and others. One difference between scalars and vectors is that with scalars elementary operations like addition, multiplication, etc are available unlike with vectors.

Vector Notation
Vectors are commonly depicted in two ways being graphically with an arrow or inside of brackets as such, $$<2, 3, 1>$$. The graphical representation is helpful in visualizing the direction and magnitude aspect of vectors while the bracket notation makes calculations much easier to do.