nubtrek

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.continue

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. continue

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.

continue

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

Voice  

Voice  



Home



Vector Component form : Revisited


 »  Vector Component Form is linear combination of vectors
    →  `i`, `j`, `k` are unit vectors
    →  `a`, `b`, `c` are scalars
    →  `vec p = a i + b j + c k` : component form is scalar multiplication and addition

Component form of Vectors

plain and simple summary

nub

plain and simple summary

nub

dummy

Vector representation is chosen to be sum of standard unit vectors multiplied by scalars.

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.




Vectors are represented in component form as sum of standard unit vectors multiplied by scalars.


Keep tapping on the content to continue learning.
Starting on learning "Component form of Vectors". ;; Vectors are represented in component form as sum of standard unit vectors multiplied by scalars.

If a person walks `3` meter north east, `4` meter north. Then, facing north, the person turns clockwise `120^@` and walk `2` meter forward. What is the distance he has to walk to return back to the starting position?vector addition first principle

  • Answer is `3+4+2`
  • answer is not `3+4+2`

The answer is 'not `3+4+2`'. The figure shows the problem using line segments and to solve this, trigonometry is used.

vector addition first principle Represent each of the segment in their horizontal and vertical components.
 •  3 meter north east = `3cos45` meter east + `3sin45` meter north

Represent each of the segment in their horizontal and vertical components.vector addition first principle
 •  `3` north east = `3cos45` east + `3sin45` north
 •  `4` north = `4cos90` east + `4sin90` north
 •  `2` at `-30^@` = `2cos(−30)` east + `2sin(−30)` north
 •  Add each of these east and north components individually
 •  `3cos45+4cos90+2cos(−30) = 3.85`
 •  `3sin45+4sin90+2sin(−30) = 5.12`
 •  result distance ` = 3.85i+5.12j`



[Continued..] What made the solution simple?

  • The vector quantities are split into components having same direction
  • The vector quantities are split into components having same magnitude

The answer is 'the vector quantities are split into components having same direction' which were easily added.

Note that a vector is given as a sum of components along three dimensions, which is equivalently a sum of scalar multiples of the three unit vectors.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Vector Component form: Component form of vector representation is the sum of standard unit vector `i`, `j`, `k` multiplied by scalars `a, b, c in RR`.
`vec p = a i + bj + ck`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

If a person walks 3 meter north east, 4 meter north. Then, facing north, the person turns clockwise 120 degree and walk 2 meter forward. What is the distance he has to walk to return back to the starting position?
1
2
The answer is ""
Represent each of the segment in their horizontal and vertical components. ;; 3 meter north east = 3 cos 45, meter east + 3 sine 45, meter north.
Represent each of the segment in their horizontal and vertical components. 3 meter north east = 3 cos 45, meter east + 3 sine 45, meter north. ;; 4 north = 4 cos 90, east + 4 sine 90 north ;; 2 at minus 30 degree = 2 cos minus 30 east + 2 sine minus 30 north.;; Add each of these east and north components individually. ;; The result is 3 point 85 i + 5. 12 j;
What made the solution simple?
1
2
The answer is 'the vector quantities are split into components having same direction' which were easily added.
Note that a vector is given as a sum of components along three dimensions, which is equivalently a sum of scalar multiples of the three unit vectors.
Vector representation is chosen to be sum of standard unit vectors multiplied by scalars.
Vector Component form: Component form of vector representation is the sum of standard unit vector i, j, k multiplied by scalars a, b, c in real numbers. ;; vector p = a i + b j + c k

we are not perfect yet...

Help us improve