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Thought-Process to Discover Knowledge

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maths >  Properties of Vector Arithmetics >  Properties of Vector Addition

Closure Property of Vector Addition

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



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What does 'closure' mean?closure property illustration

  • closed
  • not open
  • both the above
  • both the above

Answer is 'both the above'

Integer addition has closure property. It means that, if any two integers are added, the result will be within the integer set of numbers. Is it correct?closure property illustration

  • Yes, the result has to be within
  • Yes, the result has to be within
  • No, the result has to be outside

Answer is 'Result has to be within' the set of integers.

Vector space `bbb V` consists of all the vectors with real numbers as components.

Is sum of two vectors be another vector in the vector space?

  • Yes
  • Yes
  • No

The answer is 'Yes'. Sum of two real-numbers is a real number. Since vector addition is addition of real-numbers as components, sum of vectors is a vector.

 •  Sum or difference of two vectors is another vector - closed.

Closure Property of Vector Addition: For any vectors ` vec(a), vec(b) in bbb V`,
` vec(a)+vec(b) in bbb V`

                            
slide-show version coming soon