Analytic Geometry Part 2 Geometric Representation of Vectors and Algebraic Operations

Analytic Geometry Part 2 - (Geometric Representation of Vectors and Algebraic Operations 

We continue with our pre-chemometrics review of analytic geometry, noting the term vector in all cases can be represented by a matrix of r x c dimensions, where r = of rows and c = of columns. The operations defined below will be employed in future discussions. 

If M represents a vector with components (or elements) as M, My), then sM (where s is a real number, also termed a scalar ) is defined as the vector represented by (jM, sMy) and the length of is s times the length of M. One can relate the direction angles of M to those of as follows  

For the case where s 0 ( is a positive, real number), then 

In this case, the vectors sM and M have the exact opposite directions. (Note When 5 = 0, there is no definition for the vector or direction.) 

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