History of vector analysis
The "pre-Galilean vector analysis" was primarily the mathematical analysis of the movements of bodies according to the rules of vector arithmetic. The principle of kinematic became applied by Kepler to the motions of heavenly bodies, and by Galileo to the motions of bodies on the Earth's surface. Also, according to the principles of vector analysis, Galileo introduced to physics the vector product and the cross product, and formulated the laws of motion according to which the motion of any body is a combination of straight-line motion, circular motion and rotation.
Vector analysis in mathematics
Vector analysis is the study of the properties and methods for representing and manipulating vectors.
Vector algebra
Vector algebra deals with vectors and other geometrical concepts related to vectors.
Law of vector algebra
Law of vector algebra concerns itself with the properties of vector algebra such as vector identity, linearity, additivity, scalar triple product, vector triple product, law of cosines, law of sines, law of tangents, law of cosines, law of sines, law of planes, law of perpendiculars, law of parallels, law of inverse, law of reflection, law of symmetry, law of homogeneity, law of power, law of composition, law of homotheticity, law of homothesis, law of continuity, and law of homogeneity of normals, law of homogeneity of vectors, and homogeneity of scalars.
Additive identity law
Additive identity law is a vector identity:
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Additive inverse law
Additive inverse law is a vector identity:
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Vector addition
Vector addition is the sum of two vectors.
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Vector subtraction
Vector subtraction is the difference of two vectors.
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Vector multiplication
Vector multiplication is the product of two vectors.
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Vector inner product
Vector inner product is a vector expression of the scalar product of two vectors.
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Vector outer product
Vector outer product is the product of two vectors.
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