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How to prove this with respect to the angle of vectors? [closed]

1

$begingroup$

In the vector space (of 2-dimensions or 3-dimensions), vector has direction and two vectors must form a angle from $0$ to $180$ degree. Let the angle of vectors $u$ and $v$ be $theta$. We know that if $lVert urVertlVert vrVert > 0$, $costheta=cfracucdotvlVert urVertlVert vrVert$.

Here I want to prove (or disprove) that: vectors $u$ and $v$ of any dimensions get smaller angle (hence bigger $costheta$) if $u$ is updated to $u'=u+av$ where $a>0$.

This claim seems true for the 2-D or 3-D case intuitively.

Thanks.

vector-spaces

share|cite|improve this question

edited Mar 29 at 8:56

Lansiz

asked Mar 27 at 17:21

LansizLansiz

928

$endgroup$

closed as off-topic by Martin R, user296113, Javi, YiFan, Cesareo Mar 28 at 0:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, user296113, Javi, YiFan, Cesareo

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Shouldn't the angle be $cos^-1left(dfracucdotvlVert urVertlVert vrVertright)$?
  $endgroup$
  – Shubham Johri
  Mar 27 at 17:41
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Shubham Johri question modified.
  $endgroup$
  – Lansiz
  Mar 27 at 23:44
  

  
  
  
  

add a comment | 

1

$begingroup$

In the vector space (of 2-dimensions or 3-dimensions), vector has direction and two vectors must form a angle from $0$ to $180$ degree. Let the angle of vectors $u$ and $v$ be $theta$. We know that if $lVert urVertlVert vrVert > 0$, $costheta=cfracucdotvlVert urVertlVert vrVert$.

Here I want to prove (or disprove) that: vectors $u$ and $v$ of any dimensions get smaller angle (hence bigger $costheta$) if $u$ is updated to $u'=u+av$ where $a>0$.

This claim seems true for the 2-D or 3-D case intuitively.

Thanks.

vector-spaces

share|cite|improve this question

edited Mar 29 at 8:56

Lansiz

asked Mar 27 at 17:21

LansizLansiz

928

$endgroup$

closed as off-topic by Martin R, user296113, Javi, YiFan, Cesareo Mar 28 at 0:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, user296113, Javi, YiFan, Cesareo

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Shouldn't the angle be $cos^-1left(dfracucdotvlVert urVertlVert vrVertright)$?
  $endgroup$
  – Shubham Johri
  Mar 27 at 17:41
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Shubham Johri question modified.
  $endgroup$
  – Lansiz
  Mar 27 at 23:44
  

  
  
  
  

add a comment | 

$begingroup$

In the vector space (of 2-dimensions or 3-dimensions), vector has direction and two vectors must form a angle from $0$ to $180$ degree. Let the angle of vectors $u$ and $v$ be $theta$. We know that if $lVert urVertlVert vrVert > 0$, $costheta=cfracucdotvlVert urVertlVert vrVert$.

Here I want to prove (or disprove) that: vectors $u$ and $v$ of any dimensions get smaller angle (hence bigger $costheta$) if $u$ is updated to $u'=u+av$ where $a>0$.

This claim seems true for the 2-D or 3-D case intuitively.

Thanks.

vector-spaces

share|cite|improve this question

edited Mar 29 at 8:56

Lansiz

asked Mar 27 at 17:21

LansizLansiz

928

$endgroup$

share|cite|improve this question

edited Mar 29 at 8:56

Lansiz

asked Mar 27 at 17:21

LansizLansiz

928

share|cite|improve this question

edited Mar 29 at 8:56

Lansiz

asked Mar 27 at 17:21

LansizLansiz

928

asked Mar 27 at 17:21

LansizLansiz

928

asked Mar 27 at 17:21

LansizLansiz

928