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Analytic Geometry
Descartes and Fermat theorize about analytic geometry which uses separate varaibles with coordinates in three dimensional space (vectors) to solve equations. -
Newton Studies Velocity and Force
Newton derived several formulas dealing with velocity and force without relating the two as vectors. He did not connect the idea that forces have direction and magnitude which allows them to be added or multiplied. -
Vectors and Scalars Introduced
William Hamilton published a paper which introduces the terms and principles about scalars and vectors into the mathematical field. Hamilton's scalar was equal to modern day dot products, and his vector was today's cross product. -
Cross Product and Dot Product
William Clifford publishes " Elements of Dynamic" which includes cross products and dot products. -
"Elements of Vector Analysis"
Josiah Gibbs publishes this book documenting what has become today's system of vector analysis. -
Parallelogram Law
Heron writes "Mechanic" which includes the law for the addition of vectors. It is unclear whether or not he was the first to use this.