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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.

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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

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Voice

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» vector dot product of orthogonal vectors

→ `theta = 90^@`

→ `cos 90^@ = 0`

→ `vec p cdot vec q = 0`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

• Dot product of orthogonal vectors is `0`.

If dot product of two non-zero vectors is `0`, then the vectors are orthogonal.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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In this page, you will learn about the result of vector dot product of orthogonal vectors.

Starting on learning "Dot product of Orthogonal Vectors". ;; In this page, you will learn about the result of vector dot product of orthogonal vectors.

When are two vectors called 'orthogonal' vectors? `color(coral)(text(orth)) + color(deepskyblue)(text(gonia))` means `color(coral)(text(right))+color(deepskyblue)(text(angled))`.

- have `90^@` angle between them
- perpendicular to each other
- the vectors are right-angled
- all the above

The answer is 'All the above'

Given the definition of dot product as

`vec p cdot vec q = |vec p||vec q|cos theta`

What is `vec p cdot vec q`, when the given vectors are orthogonal?

- `|p||q|cos 90`
- `|p||q| 0`
- `0`
- all the above

The answer is 'All the above'.

Given two non-zero vectors `vec p, vec q in bbb V` have `vec p cdot vec q = 0`, then what is the angle between the vectors?

- `0^@`
- `90^@`
- `180^@`
- Any one of the above

The answer is '`90^@`'. It can either be `90^@` or `270^@`.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Dot Product of Orthogonal Vectors: ** For any pair of orthogonal vectors `vec p, vec q in bbb V`,

`vec p cdot vec q = 0`

**Angle between vectors when dot product is `0`:** For any pair of non-zero vectors `vec p, vec q in bbb V`, If `vec p cdot vec q = 0` then the vectors are orthogonal. The angle between them is `+- 90^@`.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Given `vec p= 2i+j-k` and `vec q = i+2j+4k` what is the angle between them?

- `90^@`
- `0`
- `180^@`
- `0^@`

The answer is '`90^@`'. As the dot product between the vectors is `0`.

Given two vectors `vec p` and `vec q` in x-y plane. They make angles `13^@` and `-77^@` with x-axis. What is `vec p cdot vec q`?

- `90`
- `0`
- `13xx77`
- `13xx(-77)`

The answer is '`0`'. The vectors are orthogonal as the angle between them is `13+77`. Note that the vectors are in x-y plane.

*your progress details*

Progress

*About you*

Progress

When are two vectors called 'orthogonal' vectors?

90;degree;angle

have 90 degree angle between them

perpendicular;each;other

perpendicular to each other

vectors;right-angled

the vectors are right-angled

all;above

all the above

The answer is 'All the above'

Given the definition of dot product as vector p dot vector q = magnitude of vector p multiplied magnitude of vector q cos theta, what is vector p dot vector q, when the given vectors are orthogonal?

1

2

3

4

The answer is 'All the above'.

Given two non-zero vectors p and q in vector space v, have vector p dot vector q = 0, then what is the angle between the vectors?

0

0 degree

90

90 degree

80;180;hundred

180 degree

Any;one;above

Any one of the above

The answer is "90 degree". It can either be 90 degree or 270 degree.

Dot product of orthogonal vectors is 0 ;; If dot product of two non-zero vectors is 0, then the vectors are orthogonal.

Dot Product of Orthogonal Vectors: For any pair of orthogonal vectors p and q in vector q ;; vector p dot vector q = 0.

Angle between vectors when dot product is 0: For any pair of non zero vectors p, q in vector space v ;; if vector p dot vector q = 0, then the vectors are orthogonal. The angle between them is plus or minus 90 degree.

Given vec p= 2i+j-k and vec q = i+2j+4k what is the angle between them?

1

2

3

4

The answer is "90 degree". As the dot product between the vectors i 0.

Given two vectors p and q in x-y plane, they make angles 13 degree and minus 77 degree with x-axis. What is vector p dot vector q?

1

2

3

4

The answer is "0". The vectors are orthogonal as the angle between them is 13+77. Note that the vectors are in x-y plane.