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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,
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  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.

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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. continue

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. continue

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. continue

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. continue

summary of this topic

Properties of Dot Product

Properties of Dot Product

Voice  

Voice  



Home




 »  vector dot product is distributive over vector addition
    →  `vec p cdot (vec q + vec r) ` ` = vec p cdot vec q ` ` + vec p cdot vec r`

Distributive Property over Vector Addition

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Dot product of sum of vectors is sum of dot products with the vectors - Distributive.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn about the distributive property of vector dot product over vector addition.


Keep tapping on the content to continue learning.
Starting on learning the property "vector dot product is Distributive over Vector Addition".

What does 'distributive' mean?distributive property illustration

  • to share; to spread
  • to restrict; to arrest

The answer is 'to share; to spread'

Given the definition of dot product as
`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`
dot product distributive property over vector addition What is `vec p cdot (vec q+vec r)`

  • `vec p cdot ((q_x+r_x)i+(q_y+r_y)j+(q_z+r_z)k)`
  • `p_x(q_x+r_x)+p_y(q_y+r_y)+p_z(q_z+r_z)`
  • `vec p cdot vec q + vec p cdot vec r`
  • all the above

The answer is 'all the above'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Distributive Property: For any given vectors `vec p, vec q, vec r in bbb V`
`color(coral)(vec p) cdot (vec q + vec r) = color(coral)(vec p) cdot vec q + color(coral)(vec p) cdot vec r`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

If the dot products of two vectors `vec a` and `vec b` with a third vector `vec c` are `2` and `3`, what is `vec c cdot (vec a + vec b)` ?

  • `5`
  • `6`
  • `2/3`
  • `3/2`

Answer is '`5`'.

your progress details

Progress

About you

Progress

What does 'distributive' mean?
share;spread
to share; to spread
restrict;arrest
to restrict; to arrest
The answer is 'to share; to spread'
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 p dot, vector q + vector r?
1
2
3
4
The answer is 'all the above'.
Dot product of sum of vectors is sum of dot products with the vectors - Distributive.
Distributive Property: For any given vectors p, q, r, in vector space v ;; vector p dot vector q + vector r =, vector p dot vector q,+, vector p dot vector r.
If the dot products of two vectors a and b with a third vector c are 2 and 3. What is vector c dot vector a + vector b?
1
2
3
4
The answer is "5"

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