nubtrek

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.continue

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. continue

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.

continue

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

Properties of Dot Product

Properties of Dot Product

Voice  

Voice  



Home




 »  equal vector dot product does not imply vectors are equal

    →  `vec p cdot vec q ` ` = vec p cdot vec r ` does not imply that `vec q = vec r`

    →  on both sides of the equation, `vec p` cannot be canceled.

    →  `vec p cdot vec q ` ` = vec p cdot vec r ` imply that `vec p cdot (vec q - vec r) = 0`

When products of two vectors are equal

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Equal dot products does not imply the vectors are equal.

 •  If dot products are equal then difference of the vectors will be perpendicular to the vector with which dot products are equal.

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.




In this page, you will learn whether vectors can be canceled in both side of the equation when two vector dot products are equal.


Keep tapping on the content to continue learning.
Starting on learning conditions in which "vector dot products of two vectors are equal". ;; In this page, you will learn whether vectors can be canceled in both side of the equation when two vector dot products are equal.

Consider real numbers `a, b in RR` and an unknown number `x`. Given that `ax = ab`, what is the value of `x`?

  • `x=a`
  • `x=b`
  • `x = a b`

The answer is '`x=b`'. Both the left hand side and right hand side of the equation is divided by `a` to arrive at the solution.

Consider vectors `vec p, vec q in bbb V` and a unknown `vec x`. Given that `vec x cdot vec p = vec q cdot vec p`. What is the value of `vec x`?vector dot product no cancellation Note: All the vectors shown in yellow-dotted-line will have the same projection on to the `vec p`.

  • cannot be calculated
  • `vec x = vec q`

The answer is 'Cannot be calculated'.

`vec x cdot vec p = vec q cdot vec p` does not imply that `vec x = vec q`.
That is, `vec p` cannot be canceled on left-hand-side and right-hand-side. vector dot product no cancellation Note that in dot product, `vec q` is split into orthogonal components and the component in parallel to `vec p` is only in the product. The component perpendicular to `vec p` is lost.

`vec x cdot vec p = vec q cdot vec p` imply that both `vec x` and `vec q` has same projection on to `vec p` shown as `a` vector dot product no cancellation If we subtract `vec x - vec q` then the common component will cancel out and the remaining vector will be perpendicular to `vec p`.

`vec x cdot vec p = vec q cdot vec p`

Subtracting `vec q cdot vec p` from both the sides. `vec x cdot vec p - vec q cdot vec p = vec q cdot vec p - vec q cdot vec p`
`(vec x - vec q)cdot vec p = (vec q - vec q)cdot vec p`
`(vec x - vec q)cdot vec p = 0 cdot vec p`
`(vec x - vec q)cdot vec p = 0 `

The above can be understood as vector `vec x - vec q` is orthogonal to `vec p`.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Cannot Cancel: Given `vec x cdot vec p = vec q cdot vec p` does not imply `vec x = vec q`. That is, the `vec p` cannot be canceled on both sides of the equation or on numerator and denominator in a division.

Subtraction on sides of an Equation: `vec x cdot vec p = vec q cdot vec p` imply that
`(vec x - vec q)cdot vec p = 0`
Which implies `vec x - vec q` is either `vec 0` or is perpendicular to `vec p`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

considers a,b in real numbers, and an unknown number x. Given that a x = a b, what is the value of x?
1
2
3
The answer is "x equals b". Both the left hand side and right hand side of the equation is divided by a to arrive at the solution.
consider vectors p, q and an unknown vector x. Given that vector x dot vector p = vector q dot vector p. What is the value of vector x?
1
2
The answer is 'Cannot be calculated'.
vector x dot vector p = vector q dot vector p does not imply that vector x = vector q. That is vector p cannot be canceled on left-hand-side and right-hand-side. ;; note that in dot product, vector q is split into orthogonal components and the component in parallel to vector p is only in the product. The component perpendicular to vector p is lost.
Equal dot products does not imply the vectors are equal.
Cannot Cancel: Given vector x dot vector p = vector q dot vector p ;; does not imply vector x = vector q. This is, vector p cannot be canceled on both sides of the equation or on numerator and denominator in a division.
vector x dot vector p = vector q dot vector p imply that both vector x and vector q has same projection on to vector p, shown as a. If we subtract vector x minus vector q, then the common component will cancel out and the remainint vector is perpendicular to vector p.
Simple manipulation of an equation involving two dot products is shown. The result that vector x - vector q is orthogonal to vector p is derived.
If dot products are equal then difference of the vectors will be perpendicular to the vector with which dot products are equal.
Subtraction on sides of an Equation: vector x dot vector p = vector q dot vector p imply that ;; vector x minus vector q, dot vector p = 0. Which implies vector x minus vector q is either vector 0 or is perpendicular to vector p.

we are not perfect yet...

Help us improve