Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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

Understanding Properties of Dot Product

»  Vector Dot Product is numerical expression of real-numbers

→  individual components on 3 axes are real numbers

→  the components multiply and add

→  properties of vector dot product is understood from the properties of real-numbers applied to the numerical expression

### Understanding Properties of Dot Product

plain and simple summary

nub

plain and simple summary

nub

dummy

Dot product is a numerical expression with terms as real numbers.

Properties of dot product is understood from properties of real numbers applied to the numerical expression representing the dot product.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.

Keep tapping on the content to continue learning.
Starting on learning - "Understanding Properties of Dot Product". ;; In this page, you will learn about the fundamentals of understanding properties of vector dot product.

Given the following
vec p = p_x i+p_yj+p_zk

vec q = q_x i+q_yj+q_zk

vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z
Where p_x, p_y, p_z, q_x, q_y, q_z in RR
Can you guess what will be the result vec p cdot vec q?

• a real number
• an integer
• a fraction
• a whole number

The answer is 'a real number'

vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z
p_x, p_y, p_z, q_x, q_y, q_z in RR

What is p_xq_x+p_yq_y+p_zq_z?

• a numerical expression with terms as real numbers
• not a numerical expression as the terms are not numbers

The answer is 'a numerical expression with terms as real numbers'

vec p cdot vec q = |p||q|cos theta

What is |p||q|cos theta?

• a numerical expression with terms as real numbers
• not a numerical expression as the terms are not numbers

The answer is 'a numerical expression with terms as real numbers'

To understand properties of dot product, the following are to be learned

•  Closure Law

•  Commutative Law

•  Associative Law

•  Distributive Law

•  Modulus in dot product

In learning these, which of the following would help?

• Memorize each of the laws
• use the properties of real numbers to understand the dot product as numerical expression

The answer is 'use the properties of real numbers to understand the dot product as numerical expression'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Dot Product as Numerical Expression: vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z
where p_x, p_y, p_z, q_x, q_y, q_z in RR
vec p cdot vec q = |p||q|cos theta
where |p|, |q|, cos theta in RR
The dot product is a numerical expression of real numbers.

Properties of Dot Product: vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z  is considered as an numerical expression and properties of real numbers are applied to understand properties of dot product.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

To understand properties of dot product, which of the following number system is used?

• Integers
• Rational numbers
• Real Numbers
• None of the above

Progress

Progress

Given the following ;; vector p = p x i + p y j + p z k ;; vector q = q x i + q y j + q z k;; vector p dot vector q = p x q x + p y q y + p z q z ;; Where p x, p y , p z, q x, q y, q z are real numbers. Can you guess what will be the result vector p dot vector q ?
real
a real number
integer
an integer
fraction
a fraction
whole
a whole number
The answer is 'a real number'
vector p dot vector q = p x q x + p y q y + p z q z ;; Where p x, p y , p z, q x, q y, q z are real numbers. What is p x q x + p y q y + p z q z?
1
2
The answer is 'a numerical expression with terms as real numbers'
vector p dot vector q = magnitude of p multiplied magnitude of q multiplied cos theta. What is the result of the dot product?
1
2
The answer is 'a numerical expression with terms as real numbers'
Dot product is a numerical expression with terms as real numbers.
Dot Product as Numerical Expression: vector p dot vector q = p x q x + p y q y + p z q z ;; where p x, p y, p z, q x, q y, q z are real numbers. ;; Vector p dot vector q = magnitude p multiplied magnitude q multiplied cos theta ;; where magnitude p, magnitude q, cos theta are real numbers ;; the dot product is a numerical expression of real numbers.
To understand properties of dot product, the following are to be learned ;; closure law ;; commutative law;; associative law;; distributive law ;; modulus in dot product. ;; In learning these, which of the following would help?
memorize;each;laws
Memorize each of the laws
use;properties;real;numbers;understand
use the properties of real numbers to understand the dot product as numerical expression
The answer is 'use the properties of real numbers to understand the dot product as numerical expression'.
Properties of dot product is understood from properties of real numbers applied to the numerical expression representing the dot product.
Properties of Dot Product: vector p dot vector q = p x q x + p y q y + p z q z ;; is considered as an numerical expression and properties of real numbers are applied to understand properties of dot product.
To understand properties of dot product, which of the following number system is used?
integers;integer
Integers
rational
Rational numbers
real
Real Numbers
none;above
None of the above