Fundamentals of Physics/Vectors

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A vector is a two-element value that represents both magnitude and direction.

Vectors are normally represented by the ordered pair or, when dealing with three dimentions, the tuple . When written in this fashion, they represent a quantity along a given axis.

The following formulas are important with vectors:

Addition and subtraction[edit]

Addition is performed by adding the components of the vector. For example, c = a + b is seen as:

With subtraction, invert the sign of the second vector's components.

Multiplication (Scalar)[edit]

The components of the vector are multiplied by the scalar:


While some domains may permit division of vectors by vectors, such operations in physics are undefined. It is only possible to divide a vector by a scalar.

As with multiplication, the components of the vector are divided by the scalar: