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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

Commutative Property of Vector Addition

In this page, commutative property of vector addition is explained.



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What does 'commute' mean?commutative property illustration

  • to go to and fro on a regular basis
  • to go to and fro on a regular basis
  • is it an English word?

The answer is 'to go to and fro between two places on a regular basis'.

Vector addition is the addition of components. The components are real numbers. commutative property illustration If the vectors are swapped in a vector addition, will the sum be same?

  • the result will be same
  • the result will be same
  • the result will change

The answer is 'the result will be same'. The real numbers are commutative. The components of vectors are real numbers and so vectors are commutative.

 •  Vectors can be swapped in vector addition - commutative.

Commutative Property of Vector Addition: For any vector `vec a, vec b in bbb V`
`vec a+vec b =vec b + vec a`

Solved Exercise Problem:

Given that `vec p + vec q = 2i-1.2j+.5k`, Which one of the following is `vec q + vec p`?.

  • `.5i-1.2j+2k`
  • `.5i+2j-1.2k`
  • `2i-1.2j+.5k`
  • `2i-1.2j+.5k`
  • `-1.2i+.5j+2k`

The answer is '`2i-1.2j+.5k`', since vector addition is commutative.

                            
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