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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

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Voice

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» vector dot product is commutative

→ `vec p cdot vec q = vec q cdot vec p`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

• Vectors can be swapped in dot product - commutative.

*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 commutative property of vector dot product.

Starting on learning the "Commutative Property of vector dot product".

What does 'commute' mean?

- to go to and fro on a regular basis
- different

The answer is 'to go to and fro between two places on a regular basis'.

Given the definition of dot product as

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

What is `vec q cdot vec p`?

- `vec p cdot vec q`
- `|p||q|cos(theta)`
- `|p||q|cos(-theta)`
- all the above

The answer is 'All the above' Note that `cos(-theta) = cos(theta)`.

Given the definition of dot product as

`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`

What is `vec q cdot vec p`?

- `vec p cdot vec q`
- `q_xp_x+q_yp_y+q_zp_z`
- `p_xq_x+p_yq_y+p_zq_z`
- all the above

The answer is 'All the above'

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Commutative Property of Dot Product: ** For any vector `vec p, vec q in bbb V`

`vec p cdot vec q =vec q cdot vec p`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Given that `vec p cdot vec q = 2.1i-1.7j+6k`, find the `vec q cdot vec p`.

- `-2.1i+1.7j-6k`
- `2.1i-1.7j+6k`
- `sqrt(2.1^2+1.7^2+6^2)`
- `2.1^2+1.7^2+6^2`

The answer is '`2.1i-1.7j+6k`' as dot product is commutative.

*your progress details*

Progress

*About you*

Progress

What does 'commute' mean?

go;fro;regular;basis

to go to and fro on a regular basis

different

different

The answer is 'to go to and fro between two places on a regular basis'.

Given the definition of dot product as

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

What is vec q cdot vec p ?

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

What is vec q cdot vec p ?

1

2

3

4

The answer is "All the above". Note that cos of minus theta = cos theta.

Given the definition of dot product as vector p dot vector q = p x q x + p y q y + p z q z ;; What is vector q dot vector p?

1

2

3

4

The answer is 'All the above'

Vectors can be swapped in dot product - commutative.

Commutative Property of Dot Product: For any vector p, q in vector space v ;; vector p dot vector q = vector q dot vector p.

Given that vector p dot vector q = 2 point 1 i minus 1 point 7 j + 6 k ; find the vector q dot vector p.

1

2

3

4

The answer is "2 point 1 i minus 1 point 7 j plus 6 k ", as dot product is commutative.