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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

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. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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.

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

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. continue

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. continue

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. continue

Voice

Voice

Home

» vector dot product NOT closed.

→ the product of vectors is a scalar

→ `vec p cdot vec q !in bbb V`

*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.

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

Answer is '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

*your progress details*

Progress

*About you*

Progress

What does 'closure' mean?

closed

closed

not;open

not open

both;above

both the above

Answer is '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.