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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.

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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 is commutative
→  vec p cdot vec q = vec q cdot vec p

### Commutative Property

plain and simple summary

nub

plain and simple summary

nub

dummy

• Vectors can be swapped in dot product - commutative.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Starting on learning the "Commutative Property of vector dot product".

What does 'commute' mean?

• to go to and fro on a regular basis
• different

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

Given the definition of dot product as
vec p cdot vec q = |vec p||vec q|cos theta
What is vec q cdot vec p?

• vec p cdot vec q
• |p||q|cos(theta)
• |p||q|cos(-theta)
• all the above

The answer is 'All the above' Note that cos(-theta) = cos(theta).

Given the definition of dot product as
vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z
What is vec q cdot vec p?

• vec p cdot vec q
• q_xp_x+q_yp_y+q_zp_z
• p_xq_x+p_yq_y+p_zq_z
• all the above

The answer is 'All the above'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Commutative Property of Dot Product: For any vector vec p, vec q in bbb V
vec p cdot vec q =vec q cdot vec p

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given that vec p cdot vec q = 2.1i-1.7j+6k, find the vec q cdot 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' as dot product is commutative.

Progress

Progress

What does 'commute' mean?
go;fro;regular;basis
to go to and fro on a regular basis
different
different
The answer is 'to go to and fro between two places on a regular basis'.
Given the definition of dot product as
vec p cdot vec q = |vec p||vec q|cos theta
What is vec q cdot vec p ?
1
2
3
4
The answer is "All the above". Note that cos of minus theta = cos theta.
Given the definition of dot product as vector p dot vector q = p x q x + p y q y + p z q z ;; What is vector q dot vector p?
1
2
3
4
The answer is 'All the above'
Vectors can be swapped in dot product - commutative.
Commutative Property of Dot Product: For any vector p, q in vector space v ;; vector p dot vector q = vector q dot vector p.
Given that vector p dot vector q = 2 point 1 i minus 1 point 7 j + 6 k ; find the vector q dot vector p.
1
2
3
4
The answer is "2 point 1 i minus 1 point 7 j plus 6 k ", as dot product is commutative.

we are not perfect yet...