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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.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Properties of Dot Product

Voice

Voice

Home

»  vector dot product NOT closed.
→  the product of vectors is a scalar
→  vec p cdot vec q !in bbb V

### Dot Product : Not Closed

plain and simple summary

nub

plain and simple summary

nub

dummy

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

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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

Keep tapping on the content to continue learning.
Starting on learning the property "dot product is not closed". ;; In this page, you will learn that the vector dot product is not closed.

What does 'closure' mean?

• closed
• not open
• both the above

What does "span" mean?

• 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

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

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

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

What does 'closure' mean?
closed
closed
not;open
not open
both;above
both the above
What does "span" mean?
full;extent;something
Full extent of something; all that is included in that;
past;tense;spin
past tense of spin
The answer is 'Full extent of something'
What is the span of vectors in 3D coordinate system?
a;i;b;j;c;k
a i + b j + c k with a,b,c as real numbers
components;vector
the components of vector taking any real number
3;dimensional;space
3 dimensional real space
all;above
all the above
The answer is 'All the above'
Vector space V consists of all the vectors with real numbers as components.
Is dot product of two vectors another vector in the vector space?
yes;s
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 a and b in vector space v ;; vector a dot vec b is not in vector space.

we are not perfect yet...