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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.
mathsVector AlgebraProperties of Dot Product

### Dot Product : Not Closed

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

click on the content to continue..

What does 'closure' mean?

• closed
• not open
• both the above
• 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