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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 Addition : Component form

» individual components add

→ `r_x = p_x+q_x`

→ `r_y = p_y+q_y`

→ `r_z = p_z+q_z`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

When vectors in the component form are added, *the corresponding components are added.*

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

You are learning the free content, however do shake hands with a coffee to show appreciation.

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In this page, learn how two vectors in component form add up.

Starting on learning "Component form of vector addition". ;; In this page, you will learn how two vectors in component form add up.

What is the component form of a vector?

- components along `x, y,` and `z` axes
- magnitude of the vector
- directional cosines of vector

Answer is 'components along `x, y,` and `z` axes'

In the component form, two vectors are considered `a i` and `p i`. What is the result of addition of two vectors `a i` and `p i` ?

- `(a+p)i`
- cannot be added.

Answer is '`(a+p)i`'. *The magnitudes add up as two vectors are in the same direction `i` , that is, along x-axis.*

What is the result of addition of two vectors `ai+bj` and `p i` ?

- `(a+p)i+bj`
- cannot be added, as the vectors are in different directions.

Answer is '`(a+p)i+bj`'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In this problem, in the direction of x-axis, `a i` and `p i` are given. They are added in magnitude.

What is the result of addition of two vectors `a i+b j+c j` and `p i+q j+r k` ?

- `(a+p)i+(b+q)j+(c+r)k`
- cannot be added, as the vectors are in different directions.

Answer is '`(a+p)i+(b+q)j+(c+r)k`'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In these two vectors, the components along the three axes are given in component form.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Addition of two vectors: ** When two vectors `vec p = p_x i+p_yj+p_zk` and `vec q = q_x i+q_yj+q_zk` are added the result is `vec p + vec q = (p_x+q_x)i + (p_y+q_y)j + (p_z+ q_z)k`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

What is the component form of a vector?

components;along;x;y;z;axes

components along x, y, and z axes

magnitude

magnitude of the vector

directional;cosines

directional cosines of vector

Answer is 'components along x, y, and z axes'

In the component form, two vectors are considered a i and p i . What is the result of addition of two vectors a i and p i ?

1

2

Answer is '(a+p) i'. ;; The magnitudes add up as two vectors are in the same direction i , that is, along x-axis.

What is the result of addition of two vectors ai+bj and p i ?

1

2

Answer is ' (a+p)i+bj '. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In this problem, in the direction of x-axis, a i and p i are given. They are added in magnitude.

What is the result of addition of two vectors a i+b j+c j and p i+q j+r k ?

1

2

Answer is ' (a+p)i+(b+q)j+(c+r)k '. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In these two vectors, the components along the three axes are given in component form.

When vectors in the component form are added, the corresponding components are added.

Addition of two vectors: When two vectors p = p x i+p y j+p z k and vector q = q x i+q y j+q z k are added the result is vector p + vector q = (p x+q x)i + (p y+q y)j + (p z+ q z)k