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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

»  Modulus of dot product is less than or equal to modulus of the vectors

→  |vec p cdot vec q| <= |vec p| |vec q|

### Property of Modulus in dot product

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Modulus of dot product is less than or equal to the product of modulus of the vectors.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Starting on learning "Property of Modulus in dot product". ;; In this page, you will learn about the property of modulus in vector dot product.

What is the modulus of dot product | vec p cdot vec q |?

• =|p| xx |q|
• <=|p| xx |q|
• >=|p| xx |q|

The answer is '<=|p| xx |q|'.
vec p cdot vec q = |p||q|cos theta
| cos theta |<= 1, so
|p||q|cos theta <= |p||q|
| vec p cdot vec q |<=|p| xx |q|

The same can be understood with geometrical meaning as given in figure. vec q = vec a + vec b
|vec q| >= |vec a|
|vec p cdot vec q | = |p||a|
|vec p cdot vec q | <= |p||q|

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Modulus Property of Dot Product: For any vectors vec p and vec q,
|vec p cdot vec q | <= |p||q|

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

What is the modulus of dot product vector p dot vector q?
1
2
3
The answer is "less than equal magnitude p multiplied magnitude q". vector p dot vector q = magnitude p multiplied magnitude q cos theta. ;; magnitude of cos theta less than or equal 1.
The same can be understood with geometrical meaning as given in figure.
Modulus of dot product is less than or equal to the product of modulus of the vectors.
Modulus Property of Dot Product: For any vectors p and q ;; magnitude of, vector p dot vector q ; less than or equal; magnitude of vector p multiplied magnitude of vector q

we are not perfect yet...