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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.

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User Guide   

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  think,
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  learn.

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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.

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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.

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exercise provides practice problems to become fluent in the concepts.

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summary of this topic

Properties of Dot Product

Properties of Dot Product

Voice  

Voice  



Home




 »  vector dot product of collinear vectors

    →  `theta = 0^@`

    →  `cos 0^@ = 1`

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

Dot product of Collinear Vectors

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Dot product of parallel vectors is product of the magnitudes of the vectors.
Dot product of anti-parallel vectors is negative of product of the magnitudes of the vectors.

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 between two collinear vectors.


Keep tapping on the content to continue learning.
Starting on learning "Dot product of Collinear Vectors". ;; In this page, you will learn about the result of vector dot product between two collinear vectors.

When two vectors are called 'collinear' vectors?collinear vectors `color(coral)(text(co)) + color(deepskyblue)(text(linear))` means `color(coral)(text(together))+color(deepskyblue)(text(on a line))`

  • the angle between vectors `0^@`
  • the angle between vectors `180^@`
  • the vectors are parallel
  • 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`
Dot product of collinear vectors What is `vec p cdot vec q`, when the given vectors are collinear?

  • `|p||q|cos 0`
  • `|p||q|cos 180`
  • one the above

The answer is 'one the above'. The angle between Collinear vectors can be either `0^@` or `180^@`.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Dot Product of Collinear Vectors: For any pair of collinear vectors `vec p, vec q in bbb V`,
If they are parallel making `0^@` angle
`vec p cdot vec q =|p||q| `

If they are anti-parallel making `180^@` angle,
`vec p cdot vec q =-|p||q| `



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given `vec p= 2i+3.1j+.5k` and `vec q = 2i+3.1j+.5k` what is the angle between them?

  • `90^@`
  • `45`
  • `180^@`
  • `0^@`

The answer is '`0^@`'. The vectors are identical.

Given a vector `vec p` with magnitude `12`, what is `vec p cdot vec p`?

  • `12`
  • `sqrt(12)`
  • `12xx12`
  • `12 cos 0`

The answer is '`12xx12`'.

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Progress

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Progress

When two vectors are called 'collinear' vectors?
1
2
3
4
The answer is "All the above".
Given the definition of dot product as vector p dot vector q =, magnitude of vector p, magnutude of vector q, cos theta. What is vector p dot vector q, when the given vectors are collinear?
1
2
3
The answer is "one of the above". The angle between collinear vectors can be either 0 degree or 180 degree.
Dot product of parallel vectors is product of the magnitudes of the vectors. ;; Dot product of anti-parallel vectors is negative of product of the magnitudes of the vectors.
Dot Product of Collinear Vectors: for any pair of collinear vectors p and q in vector space v, if they are parallel making 0 degree angle ;; vector p dot vector q = magnitude p, magnitude q. ;; If they are anti-parallel making 180 degree angle, vector p dot vector q = minus magnitude of p, magnitude of q.
Given vector p = 2 i + 3 point 1 j + point 5 k and, vector q = 2i+3 point 1 j + 0.5k, what is the angle between them?
1
2
3
4
The answer is "0 degree". The vectors are identical.
Given a vector p with magnitude 12, what is vector p dot vector p?
1
2
3
4
The answer is "12 multiplied 12".

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