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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.

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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

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

think,

figure-out, &

learn.

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.

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» vector cross product is NOT associative

→ `vec p xx (vec q xx vec r) ``!= (vec p xx vec q)xx vec r`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

• Cross product is not associative.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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In this page, you will learn that the vector cross product is not associative.

Starting on learning "vector Cross product is not associative".

What is associative property of an operator `***`?

- `(x *** y) *** z = x *** (y *** z)`
- `x *** y = y *** x`
- `x *** y = - y *** x`

The answer is '`(x *** y) *** z = x *** (y *** z)`'. The element `y` in the equation is associated with `x` first in the left-hand-side, where as it is associated with `z` first in the right-hand-side.

The vector cross product is not associative. It is proven with one simple example.

Consider two non-zero vectors `vec p` and `vec q`.

`vec p xx vec p = 0`

and so `(vec p xx vec p) xx vec q = 0`

But, `vec p xx vec q` is perpendicular to `vec p`

So `vec p xx (vec p xx vec q) !=0`

It is proven that (vec p xx vec p) xx vec q !=vec p xx (vec p xx vec q)

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Not Associative: ** For any vector `vec p, vec q, vec r in bbb V`

`(vec p xx vec q) xx vec r != vec p xx (vec q xx vec r)`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Consider `(vec x xx vec y) xx vec z` `= vec p xx (vec q xx vec z)`. Can the vector `vec z` be canceled on either side of the equation?

- Yes
- No

The answer is 'No'.

*your progress details*

Progress

*About you*

Progress

What is associative property of an operator star?

1

2

3

The answer is "x star y, star z, = , x star, y star z". The element y in the equation is associated with x first in the left-hand-side, where as it is associated with z first in the right hand side.

The vector cross product is not associative. It is proven with one simple example. ;; Consider two non-zero vectors p and q. vector p cross vector p = 0;; so vector p cross vector p, cross vector q = 0;; but vector p cross vector q is perpendicular to vector p. So vector p cross, vector p cross vector q not equals 0. It is proven that the cross product is not associative.

Cross product is not associative.

Not Associative: For any vector p, q, r in vector space V, vector p cross vector q, cross vector r != vector p cross, vector q cross vector r.

Consider the given equation. Can the vector z be canceled on either side of the equation?

yes;s

Yes

no

No

The answer is 'No'.