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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 is NOT associative
→  vec p cdot (vec q cdot vec r)   != (vec p cdot vec q) cdot vec r

### Not Associative

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Dot product is not associative.

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 associative.

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

What is associative property of an operator ***?

• (x *** y) *** z = x *** (y *** z)
• x *** y = y *** x
• x *** y = - y *** x

The answer is '(x *** y) *** z = x *** (y *** z)'. In the left hand side of the equation, y is associated with x first, where in the right hand side, y is associated with z first.

Dot product cannot be considered for associative property. Consider the two (vec p cdot vec q) and vec r. The first term in parenthesis is a scalar and the second term is a vector.

The dot product is not defined between a scalar and a vector.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Not Associative: For any vector vec p, vec q, vec r in bbb V
(vec p cdot vec q) vec r != vec p (vec q cdot vec r)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Consider (vec x cdot vec y) vec z = vec p (vec q cdot vec z). Can the vector vec z be canceled on either side of the equation?

• Yes
• No

The answer is 'No'. The vec z can be canceled in (vec x cdot vec y) vec z = (vec p cdot vec q) vec z. Since associative property is not defined for dot product, the equation given in the question can not be equivalently expressed in this form.

Progress

Progress

What is associative property of an operator star?
1
2
3
The answer is "x star y, star z = x star, y star z". In the left hand side of the equation, y is associated with x first, where as in the right hand side, y is associated with z first.
Dot product cannot be considered for associative property. Consider the two, vector p dot vector q and vector r. The first term in parenthesis is a scalar and the second term is a vector. The dot product is not defined between a scalar and a vector.
Dot product is not associative.
Not Associative: for any vectors p, q, r in vector space v; vector p dot vector q, multiplied vector r; not equals ; vector p multiplied, vector q dot vector r.
Consider vector x dot vector y, vector z = vector p, vector q dot vector z. Can the vector z be canceled on either side of the equation?
1
2
The answer is "No". The vector z can be canceled in vector x dot vector y, multiplied vector z = vector p dot vector q multiplied vector z. ;; Since associative property is not defined for dot product, the equation given in the question can not be equivalently expressed in this form.

we are not perfect yet...