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Thought-Process to Discover Knowledge

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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.continue

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.continue

Welcome to **nub****trek**.

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The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

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exercise.

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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`

*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

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In this page, learn in detail about basics of 'vector multiplication'.

Starting on learning basics of "Multiplication of Vectors". ;; In this page, learn in detail about basics of vector multiplication.

What are the fundamental operations of mathematics?

- Addition and Subtraction
- Multiplication and Division
- all the above

The answer is 'All the Above'. The four fundamental operations of mathematics are Addition, Subtraction, Multiplication, and Division.

We have studied about vector addition and multiplication of vectors by a scalar.

Is there something as vector multiplication?

That is the subject of learning in these pages. Let us go through some basics to understand vector multiplication.

Consider the `vec p` and `vec q` shown in figure. `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`

When the vectors `vec p` and `vec q` interact as a product which component(s) of `vec q` take part in the multiplication?

- only `vec a`
- only `vec b`
- either one : `vec a` or `vec b`
- both together : `vec a` and `vec b`

The answer is 'either one : `vec a` or `vec b`'. Remember the orthogonality of directions. When vectors interact to form products the interaction is either with the component in parallel or the component in perpendicular.

Orthogonality of Directions : Any change in a direction affects component along that direction only and does not affect the components in the directions at `90^@` to that direction.

The component which is in perpendicular to a direction does not affect the component in the direction. The directions which are at `90^@` angle are referred to as orthogonal directions.

In arithmetic operations like addition, subtraction, multiplication by a scalar, and product of vectors, – the results are computed for

• ** components in parallel**

• **components in perpendicular **

Each of these two components interact differently.

*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

*your progress details*

Progress

*About you*

Progress

What are the fundamental operations of mathematics?

addition;subtraction

Addition and Subtraction

multiplication;division

Multiplication and Division

all;above

all the above

The answer is 'All the Above'. The four fundamental operations of mathematics are Addition, Subtraction, Multiplication, and Division.

We have studied about vector addition and multiplication of vectors by a scalar.;; Is there something as vector multiplication? ; That is the subject of learning in these pages. Let us go through some basics to understand vector multiplication.

Consider the vector p and vector q shown in figure. Vector q is split into vector a and vector b, such that ;; vector q = vector a + vector b and ;; vector a is in parallel to vector p ;; vector b is in perpendicular to vector p. ;; When vectors p and q interact as a product which component or components of vector q take part in the multiplication?

1

2

3

4

The answer is "Either one : vector a or vector b". Remember the orthogonality of directions. When vectors interact to form products the interactionis either with the component in parallel or the component in perpendicular.

Orthogonality of Directions : Any change in a direction affects component along that direction only and does not affect the components in the directions at 90 degree to that direction. ;; The component which is in perpendicular to a direction does not affect the component in the direction. The directions which are at 90 degree angle are referred to as orthogonal directions.

In arithmetic operations like addition, subtraction, multiplication by a scalar, and product of vectors, – the results are computed for ;; components in parallel ;; components in perpendicular ;; Each of these two components interact differently.

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. Multiplicand vector p and multiplier vector q are given. ;; Vector q is split into vector a and vector b, such that vector q = vector a + vector b and ;; 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 = vector p dot vector a ;; another with component in perpendicular to the vector, called vector cross product. vector p cross vector q = vector p cross vector b