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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   

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
  think,
  figure-out, &
  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.

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. continue

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. continue

summary of this topic

Vector Cross Product

Vector Cross Product

Voice  

Voice  



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Cross Product With Direction Removed


 »  By definition, cross product is a vector


 »  Some applications may specify a scalar in the multiplication of components in perpendicular. In such cases, the direction is removed.

Cross Product with Direction removed

plain and simple summary

nub

plain and simple summary

nub

dummy

Vector cross product, by definition, is a vector. Depending on the application requirement, the direction can be removed.

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 removing the direction of the vector cross product with an example application.


Keep tapping on the content to continue learning.
Starting on learning "Cross Product with Direction removed". ;; In this page, you will learn about removing the direction of the vector cross product with an example application.

An object by position vector `vec p` is at a distance from a screen. The screen is given by unit vector `vec s`vector cross product distance example Is the distance of the object from the screen a vector or scalar?

  • a vector
  • a scalar

The answer is 'a vector'. The distance is a vector that terminates at the object and at `90^@` angle to the screen.

Note: In physics - Kinematics, distance and displacement are defined as scalar and vector. In coordinate geometry, distance from an object to another is a vector.

Given `vec p` and the screen `hat s`.vector cross product distance example what is the magnitude of distance of object from the screen?

  • `|vec p xx hat s|`
  • `|p| sin theta`
  • both the above

The answer is 'Both the above'.

An object by position vector `vec p` is at a distance from a screen. The screen is given by unit vector `vec s` We saw that the distance is a vector and the length of the distance is `|vec p xx hat s|`.vector cross product distance example What is the direction of the distance vector?

  • unit vector along `vec p - (vec p cdot hat s) hat s`
  • Direction cannot be found

The answer is 'unit vector along `vec p - (vec p cdot hat s) hat s`'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Distance using Cross Product: For a vector `vec p` and a direction given by unit vector `hat s`, the magnitude of distance of point given by `vec p` to the direction `hat s` is `|vec p xx hat s|`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

An object by position vector p is at a distance from a screen. The screen is given by unit vector s. IS the distance of the object from the screen a vector or scalar?
vector
a vector
scalar
a scalar
The answer is "a vector". The distance is a vector that terminates at the object and at 90 degree angle to the screen. ;; Note: In physics - Kinematics, distance and displacement are defined as scalar and vector. In coordinate geometry, distance from an object to another is a vector.
Given vector p and the screen s hat. What is the magnitude of distance of object from the screen?
1
2
3
The answer is 'Both the above'.
An object by position vector p is at a distance from a screen. The screen is given by unit vector s, we saw that the distance is a vector and the length of the distance is magnitude of vector p cross s hat. What is the direction of the distance vector?
1
2
The answer is "unit vector along vector p minus, vector p dot s hat".
Vector cross product, by definition, is a vector. Depending on the application requirement, the direction can be removed.
Distance using Cross Product: For a vector p and a direction given by unit vector s, the magnitude of distance of point given by vector p to the direction s is magnitude of vector p cross vector s.

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