Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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

### Vector Cross Product

Voice

Voice

Home

Multiplication of Vectors

»  Two products because of orthogonality of components of vectors
→  dot product is defined for components in parallel vec p cdot vec q =vec p cdot vec a
→  cross product is defined for components in perpendicular vec p xx vec q =vec p xx vec b

### Introduction to Cross Product

plain and simple summary

nub

plain and simple summary

nub

dummy

When two vector quantities interact to form a product, either one of the (1) component in parallel or (2) component in perpendicular is involved in the multiplication. In practical scenarios, when one component interacts, the other component does not interact and is lost in the product.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.

Keep tapping on the content to continue learning.
Starting on learning "Introduction to Cross Product". ;; In this page, learn in detail about basics of 'vector cross product' with an example.

We have learned that Vector dot product is defined as multiplication of components in parallel. This definition provides mathematical model for the cause and effect which are in the same direction.

A person takes 3 oranges that costs 10 coins each. How much the person has to pay for the fruits?

• 40 coins
• 30 coins
• 10 coins
• 50 coins

The answer is '30' coins. The scalar quantity 3 multiplies with another scalar quantity 10.

Two different scalar quantities can be multiplied.

That is, two different quantities are multiplied. One quantity is independent of another.

In the case of vectors too, two quantities can interact. The quantities need not be related and are independent of one another.

Effect of direction : In mathematical calculations, vectors have the following properties

•  A vector is represented as components along orthogonal directions.

•  Two types of vector multiplication are defined for component in parallel and component in perpendicular.

The vector components in parallel form a product called dot product. Vector dot product has meaning or practical application -- cause and effect are in parallel.

Similar to that, does vector cross product has any meaning or practical application? OR is that just an abstraction?
Consider the field of standing crops and a blade is cutting the crop at an angle. Cross product (in which components in perpendicular interact) can be understood with the following

•  If the blade runs at right angle to the crop, then it cuts maximum

•  If the blade cuts vertically in parallel to the crop, it does not cut any crop

•  If the blade cuts at an angle theta, then the crop cut is in proportion to the component in perpendicular to the crop

And, of course, the cross product is also used in the abstract form to compute products between vectors.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

How does direction affect vector quantities in multiplication? At an abstract level, there are two products possible. Given multiplicand vec p and multiplier vec q. vec q is split into vec a and vec b, such that
vec q = vec a + vec b and
vec a is in parallel to vec p
vec b is in perpendicular to vec p

two forms of multiplications are defined for each of these two components.

•  one with component in parallel to the other, called vector dot product.vec p cdot vec q = vec p cdot vec a

•  another with component in perpendicular to the vector, called vector cross product. vec p times vec q = vec p times vec b

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

We have learned that Vector dot product is defined as multiplication of components in parallel. This definition provides mathematical model for the cause and effect which are in the same direction. ;;In this page, vector cross product is introduced step-by-step.
A person takes 3 oranges that costs 10 coins each. How much the person has to pay for the fruits?
40
40 coins
30
30 coins
10
10 coins
50
50 coins
The answer is "30 coins". The scalar quantity 3 multiplied with another scalar quantity 10. ; Two different scalar quantities can be multiplied.
That is, two different quantities are multiplied. One quantity is independent of another. In the case of vectors too, two quantities can interact. The quantities need not be related and are independent of one another.
Effect of direction: In mathematical calculations, vectors have the following properties ;; A vector is represented as components along orthogonal directions.;; In vector addition, components in parallel add up.;; Two types of vector multiplication are defined for component in parallel and component in perpendicular.
The vector components in parallel form a product called dot product. Vector dot product has meaning or practical application -- cause and effect are in parallel. ;; Similar to that, does vector cross product has any meaning or practical application? OR is that just an abstraction? ;; Consider the field of standing crops and a blade is cutting the crop at an angle. Cross product (in which components in perpendicular interact); can be understood with the following ;; If the blade runs at right angle to the crop, then it cuts maximum ;; If the blade cuts vertically in parallel to the crop, it does not cut any crop ;; If the blade cuts at an angle theta, then the crop cut is in proportion to the component in perpendicular to the crop ; And, of course, the cross product is also used in the abstract form to compute products between vectors.
When two vector quantities interact to form a product, either one of the ;; component in parallel or ;; component in perpendicular is involved in the multiplication. In practical scenarios, when one component interacts, the other component does not interact and is lost in the product.
How does direction affect vector quantities in multiplication? At an abstract level, there are two products possible. Given multiplicand vector p and multiplier vector q. Vector q is split into vector a and vector b, such that ;; vector q = vector a + vector b ;; vector a is in parallel to vector p; vector b is in perpendicular to vector p;; two forms of multiplications are defined for each of these two components. ;; one with component in parallel to the other, called vector dot product. vector p dot vector q = p multiplied a ;; another with component in perpendicular to the vector, called vector cross product. vector p cross vector q = p multiplied b as vectors.

we are not perfect yet...