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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.

Read in the blogs more about the unique learning experience at nubtrek.

User Guide

Welcome to nubtrek.

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.

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.

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.

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.

User Guide

jogger provides the complete mathematical definition of the concepts.

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.

User Guide

exercise provides practice problems to become fluent in the concepts.

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.

summary of this topic

### 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? 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
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'.

Progress

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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