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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 with null vector
→  vec p cdot vec 0 = 0

### Dot product with a null vector

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Dot product with a null vector results in a null vector.

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 with a null vector.

Keep tapping on the content to continue learning.
Starting on learning "Dot product with a null vector". ;; In this page, you will learn about the result of vector dot product with a null vector.

What is a null vector or zero vector?

• A vector of magnitude 0
• 0i+0j+0k
• vec 0
• 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 0)?

• null vector
• vec p
• |vec p|
• all the above

The answer is 'Null Vector' As |vec 0| = 0, the dot product is 0.

Given the definition of dot product as
vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z
What is vec p cdot (vec 0)?

• vec 0
• vec p
• p_x+p_y+p_z
• all the above

The answer is 'vec 0' As all the x, y, z components of vec 0 is 0, the dot product is 0.

Dot product with null vector: For any vector vec p in bbb V
vec p cdot vec 0 = 0

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given that vec x has unknown magnitude and direction. What is the result of vec 0 cdot vec x?

• unknown
• 0
• vec 0

The answer is '0'.

Progress

Progress

What is a null vector or zero vector?
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 multiplied magnitude of vector q cos theta, what is vector p dot vector 0?
1
2
3
4
The answer is "Null vector", As magnitude of vector 0 = 0, the dot product is 0.
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 p dot vector 0?
1
2
3
4
The answer is "vector 0". As all the x y z components of vector 0 is 0, the dot product is 0.
Dot product with a null vector results in a null vector.
Dot product with null vector: for any vector p in vector space v ;; vector p dot vector 0 = 0.
Given that vector x has unknown magnitude and direction, what is the result of vector 0 dot vector x?
1
2
3
The answer is ' 0 '.

we are not perfect yet...