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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

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» Vector Cross Product is NOT commutative

→ `vec p xx vec q != vec q xx vec p`

→ `vec p xx vec q = - vec q xx vec p`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

• In a cross product if the vectors are swapped, the result is negative of the product. - not commutative.

*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 cross product is not commutative.

Starting on learning, "cross product is not commutative". ;; In this page, you will learn that the vector cross product is not commutative.

What does 'commute' mean?

- to go to and fro on a regular basis
- it does not mean anything

The answer is 'to go to and fro between two places on a regular basis'.

Given the definition of cross product as

`vec p xx vec q = |vec p||vec q|sin theta hat n`

What is `vec q xx vec p`?

- `vec p xx vec q`
- `|p||q|sin(theta) hat n`
- `|p||q|sin(-theta) hat n`
- all the above

The answer is '`|p||q|sin(-theta) hat n`'. The angle traversed from `vec q` to `vec p` is `-theta`.

Given the definition of cross product as

`vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`

What is `vec q xx vec p`?

- `-vec p xx vec q`
- `|(i, j, k),(q_x, q_y, q_z),(p_x, p_y, p_z)|`
- `-|(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`
- all the above

The answer is 'All the above'

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Not Commutative: ** For any vector `vec p, vec q in bbb V`

`vec p xx vec q = - vec q xx vec p`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Given that `vec p xx vec q = 2.1i-1.7j+6k`, find the `vec q xx vec p`.

- `-2.1i+1.7j-6k`
- `2.1i-1.7j+6k`
- `sqrt(2.1^2+1.7^2+6^2)`
- `2.1^2+1.7^2+6^2`

The answer is '`-2.1i+1.7j-6k`'.

*your progress details*

Progress

*About you*

Progress

What does 'commute' mean?

go;fro;regular

to go to and fro on a regular basis

does;not;mean

it does not mean anything

The answer is 'to go to and fro between two places on a regular basis'.

Given the definition of cross product as vector p cross vector q =; magnitude of p, magnitude of q, sine theta, n hat; What is vector q cross vector p?

1

2

3

4

The answer is "magnitude of p, magnitude of q, sine minus theta, n hat". The angle traversed from vector q to vector p is minus theta.

Given the definition of cross product as vector p cross vector q in determinant form; What is vector q cross vector p?

1

2

3

4

The answer is 'All the above'

In a cross product if the vectors are swapped, the result is negative of the product. - not commutative.

Not Commutative: For any vector p, q in vector space v, vector p cross vector q = minus vector q cross vector p.

Given that vector p cross vector q = 2 point 1 i minus 1 point 7 j + 6 k ; find the vector q cross vector p.

1

2

3

4

The answer is "minus 2 point 1 i + 1 point 7 j minus 6 k".