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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsVector AlgebraProperties of Dot Product

Dot Product : Not Closed

In this page, you will learn that the vector dot product is not closed.



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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'

What does "span" mean?

  • Full extent of something; all that is included in that;
  • Full extent of something; all that is included in that;
  • past tense of spin

The answer is 'Full extent of something'

What is the span of vectors in 3D coordinate system?

  • `ai+bj+ck` with `a,b,c in RR`
  • the components of vector taking any real number
  • `RR^3`
  • all the above
  • all the above

The answer is 'All the above'

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

Is dot product of two vectors another vector in the vector space?

  • Yes
  • No
  • No

The answer is 'No'. Dot product of two vectors is a scalar real number.

 •  Dot product of two vectors is a scalar and not a vector - not closed.

Dot Product is Not Closed: For any vectors ` vec(a), vec(b) in bbb V`,
` vec(a)cdot vec(b) !in bbb V`

                            
slide-show version coming soon