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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 Vector Multiplication by Scalar

Voice

Voice

Home

»  multiplication of a vector by a scalar is distributive over scalar addition
→  (lambda + mu) vec p = lambda vec p + mu vec p

plain and simple summary

nub

plain and simple summary

nub

dummy

•  A vector multiplied by sum of two scalars equals sum of the vector multiplied by the scalars.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Starting on learning the property "Distributive over Scalar Addition". ;; In this page, The property, Multiplication of vector is distributive over scalar addition, is explained.

What does 'distribute' mean?

• to trouble or disturb
• to give to many

The answer is 'to give to many'.

Considering that a vector has components as real numbers, Given that vec p = ai+bj+ck and lambda + mu where a,b,c,lambda,mu in bbb R, What will be the result of (lambda + mu) vec p?

• scalar
• lambda vec p + mu vec p
• lambda + mu vec p

The answer is 'lambda vec p + mu vec p'. This can be proven by multiplying the components individually by the scalar and using vector addition properties.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Distributive Over scalar addition: Given scalars lambda,mu and vector vec p,
(lambda+mu)vec p = lambda vec p + mu vec p

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given that vec p = 3 vec q and vec r = 2 vec q, which of the following equals 7 vec q?

• vec p + vec r
• vec p + 2 vec r
• vec p - vec r
• vec r - vec p

The answer is 'vec p + 2 vec r'

Progress

Progress

What does 'distribute' mean?
trouble;disturb
to trouble or disturb
give;many
to give to many
The answer is 'to give to many'.
Considering that a vector has components as real numbers. Given that vector p = a i+b j+c k and lambda + mu; where a,b,c,lambda,mu are in real numbers. What will be the result of lambda + mu multiplied vector p?
1
2
3
The answer is "lambda multiplied vector p plus mu multiplied vector p". This can be proven by multiplying the components individually by the scalar and using vector addition properties.
A vector multiplied by sum of two scalars equals sum of the vector multiplied by the scalars.
Distributive Over scalar addition: Given scalars lambda,mu and vector p ;; lambda plus mu multiplied vector p ;=; lambda multiplied vector p plus mu multiplied vector p
Given that vector p = 3 times vector q and vector r = 2 times vector q, which of the following equals 7 times vector q?
1
2
3
4
The answer is "vector p + 2 times vector r"

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