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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,
  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.

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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

Multiplication of Vectors by Scalar

Multiplication of Vectors by Scalar

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Vector as Sum of Vectors


 »  numerical expression in place of numbers
    →  `2` can be represented with `4-2` or `34/17`
All these represent the same number.


 »  Vectors as Linear combination of vectors
    →  `3 sqrt(2)` at `45^@` angle
    →  `3` at `0^@` + `3` at `90^@`
    →  `6` at `90^@` + `3sqrt(2)` at `-45^@`
All these represent the same vector.

Vector as sum of vectors

plain and simple summary

nub

plain and simple summary

nub

dummy

A vector can be equivalently given as the sum of vectors.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, you will learn that Vectors can be represented as sum of several vectors.


Keep tapping on the content to continue learning.
Starting on learning "Vector as sum of vectors". ;; In this page, you will learn that Vectors can be represented as sum of several vectors.

Which of the following is the largest number?

  • `5`
  • `2+3`
  • `6-1`
  • All the above

Answer is 'all the above'.
A quantity can be equivalently represented with a number or combination of several numbers.

Three persons, starting from a common point, are walking
 •  Person A walks at an angle `45^@` for `3xx sqrt2` meter
 •  Person B walks `3` meter at an angle `0^@` and then 3 meter at an angle `90^@`
 •  Person C walks `6` meter at an angle `90^@` and then `3 xx sqrt2` meter at an angle `−45^@`

To walk to the starting point, all three has to walk ____linear combination of vectors

  • same distance but different directions
  • same distance in the same direction
  • different distances in the same direction
  • different distances in different directions

Answer is 'same distance in the same direction'. A vector quantity can be equivalently represented by combination of several vectors.

Three persons, starting from a common point, are walking
 •  Person A walks at an angle `45^@` for `3xx sqrt2` meter
 •  Person B walks `3` meter at an angle `0^@` and then 3 meter at an angle `90^@`
 •  Person C walks `6` meter at an angle `90^@` and then `3 xx sqrt2` meter at an angle `−45^@`.linear combination of vectors What describes the walk of Person A?

  • One vector quantity `3sqrt2` at angle `45^@`
  • Sum of two vector quantities `3sqrt2` and angle `45^@`

The answer is 'One vector quantity'.

Three persons, starting from a common point, are walking
 •  Person A walks at an angle `45^@` for `3xx sqrt2` meter
 •  Person B walks `3` meter at an angle `0^@` and then 3 meter at an angle `90^@`
 •  Person C walks `6` meter at an angle `90^@` and then `3 xx sqrt2` meter at an angle `−45^@` linear combination of vectors What describes the walk of Person B?

  • two vector quantities `3` at `0^@` and `3` at `90^@`
  • two vector quantities `6` at `90^@` and `3sqrt2` at `-45^@`

Answer is 'two vector quantities `3` at `0^@` and `3` at `90^@`'.

Note that person A’s and person B’s walks are specified by one vector quantity and two vector quantities. Still, they are at the same distance and direction from the starting point. Effectively, their return to the starting point can be specified by one identical vector quantity.

In scalar quantities, person A has `3` apples in a basket. Person B has `2` apples in one hand and `1` apple in another hand. Who has more apples?

  • Person A
  • Person B
  • both have the same number of apples

The answer is 'both have the same number of apples', which is understood as `2+1 = 3`.

Given vectors
`vec x = 2i+3j+4k`

`vec y = -1i-1j-2k`

`vec z = i+2j+2k`
What is `vec x+vec y`?

  • i-2j+2k
  • i+2j+2k
  • 3i+4j+6k
  • none of the above

answer is '`i+2j+2k`'. Note that the result is same as `vec z`. Reiterating that A vector can be equivalently given as a sum of vectors.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Linear Combination of Vectors: A vector can be equivalently represented as sum of vectors.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

Which of the following is the largest number?
5
5
2;3;plus
2+3
6;minus;1
6 minus 1
all;the;above
All the above
The answer is "all the above". A quantity can be equivalently represented with a number or combination of several numbers.
three persons, starting from a common point, are walking ;; person a walks at an angles 45 degree for 3 times square root 2 meter;; person b walks 3 meter at an angle 0 degree and then 3 meter at an angle 90 degree;; person c walks 6 meter at an angle 90 degree and then 3 times square root 2 meter at an angle minus 45 degree. ;; To walk to the starting point, all three has to walk ...
1
2
3
4
The answer is "same distance in the same direction". A vector quantity can be equivalently represented by combination of several vectors.
What describes the walk of Person A?
1
2
The answer is 'One vector quantity'.
What describes the walk of Person B?
1
2
The answer is "two vector quantities 3 at 0 degree and 3 at 90 degree".
Note that person A’s and person B’s walks are specified by one vector quantity and two vector quantities. Still, they are at the same distance and direction from the starting point. Effectively, their return to the starting point can be specified by one identical vector quantity.
In scalar quantities, person A has 3 apples in a basket. Person B has 2 apples in one hand and 1 apple in another hand. Who has more apples?
a
Person A
b
Person B
both;have;same;number;apples
both have the same number of apples
The answer is 'both have the same number of apples', which is understood as 2+1 = 3 .
Given vectors: x = 2 i + 2 j + 4 k ; vector y = minus 1 i minus 1 j minus 2 k ; vector z = i + 2j + 2k ; What is vector x plus vector y?
1
2
3
4
The answer is "i + 2j + 2k". Note that the result is same as vector z. Reiterating that A vector can be equivalently given as a sum of vectors.
A vector can be equivalently given as the sum of vectors.
Linear Combination of Vectors: A vector can be equivalently represented as sum of vectors.

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