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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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mathsVector AlgebraProperties of Vector Addition

Properties of vector addition

In this page, summary of all the properties of vector addition is explained.

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Vectors are quantities with magnitude and direction. It is mathematically represented as components along 3 axes.
What numbers are used as components of vectors?

  • integers
  • rational numbers
  • real numbers
  • real numbers

Answer is 'real numbers'.

Vector addition is addition of individual components respectively. Since the components are real-numbers, Vector addition is equivalently real-number addition in multiple dimensions. It does not involve any trigonometric or other such manipulations.

Vector addition is equivalently addition of real-numbers as components.
Properties of vector addition are closely related to the properties of real-number addition.

Vector addition as addition of Real Numbers: Vector addition is equivalently addition of components that are real numbers.
Properties of vector addition is understood by applying the properties of real-number addition on the components.

Properties of Vector addition:

 •  Closure Property

 •  Commutative Property

 •  Associative Property

 •  Additive identity

 •  Additive Inverse

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