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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.

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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

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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 Cross Product

Voice

Voice

Home

»  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

### Cross Product : Not Commutative

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.

Keep tapping on the content to continue learning.
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'.

Progress

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".

we are not perfect yet...