algebra : Scalars and Vectors

May 29th, 2015
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Mathematics is the language of physics. With it, we can quantitatively describe the world around us. In mechanics, we will use two types of quantities to represent concepts like force, mass and time numerically.

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Scalars and VectorsMathematics is the language of physics. With it, we can quantitatively describe the world around us. In mechanics, we will use two types of quantities to represent concepts like force, mass and time numerically. These two types are known as scalars and vectors.GoalsLearn the definitions of scalars and vectors. See some examples of vector and scalar quantities.Translate vectors to and from their components.Understand how to add, subtract and multiply vectors.DefinitionsScalar:Scalars are used to describe one dimensional quantities, that is, quantities which require only one number to completely describe them. Examples of scalar quantities are:TemperatureTimeSpeedMassLocation Along a Line (1D)Vector:Vectors are used to describe multi-dimensional quantities. Multi-dimensional quantities are those which require more than one number to completely describe them. Vectors, unlike scalars, have two characteristics, magnitude and direction. Examples of vector quantities are:Location in a Plane (2D)Location in Space (3D)VelocityAccelerationForceNote:The drawings on this page contain many vector diagrams. We will use colors to distinguish what each vector represents. The table below shows the color scheme that we will be using from now on.Vector ColorMeaningArbitrary Vectors(Red)Vectors in X Direction(Blue)Vectors in Y Direction(Green)Resultant Vectors(Black)Coordinate Axes(Gray)Vector DiagramsWe use vector diagrams to v

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