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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

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

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

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

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

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

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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

*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

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

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?

- 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.

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.

• `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