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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 Vector Multiplication by Scalar

Voice

Voice

Home

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

plain and simple summary

nub

plain and simple summary

nub

dummy

•  A scalar multiplied by sum of two vectors equals sum of vectors multiplied by the scalar.

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 Vector Addition". ;; In this page, the property, multiplication of scalar is distributive over vector addition, is explained.

Considering that a vector has components as real numbers, Given that vec p = ai+bj+ck, vec q = e i + fj + g k and lambda  where a,b,c,d,e,f,lambda in bbb R, What will be the result of lambda (vec p + vec q)?

• scalar
• lambda vec p + lambda vec q
• lambda vec p + vec q

The answer is 'lambda vec p + lambda vec q'. This is 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 Vector Addition: Given scalar lambda and vectors vec p, vec q,
lambda(vec p + vec q) = lambda vec p + lambda vec q

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given that vec p = 6 vec q and vec r = 4 vec s, which of the following equals 3 ( 2vec q+ 4/3 vec s)?

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

The answer is 'vec p + vec r'.

Progress

Progress

Considering that a vector has components as real numbers. Given that vector p = a i+b j+c k, vector q = e i + f j + g k and lambda where a,b,c,d,e,f,lambda are in real numbers, ;; What will be the result of lambda multiplied vector p + vector q?
1
2
3
The answer is "lambda multiplied by vec p + lambda multiplied by vec q ". This is proven by multiplying the components individually by the scalar and using vector addition properties.
A scalar multiplied by sum of two vectors equals sum of vectors multiplied by the scalar.
Distributive over Vector Addition: Given scalar lambda and vectors p, vector q, lambda multiplied (vector p + vector q) = lambda times vector p + lambda times vector q
Given that vector p = 6 times vector q and vector r = 4 times vector s, which of the following equals 3 times, 2 vector q + 4 by 3 vector s?
1
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The answer is "vector p plus vector r".

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