Notices
Results 1 to 7 of 7
Like Tree1Likes
  • 1 Post By Markus Hanke

Thread: Question about vectors?

  1. #1 Question about vectors? 
    Forum Freshman
    Join Date
    Feb 2013
    Posts
    15
    Can you divide by vectors? If so, how? For instance, in F=ma, F and a are vectors, so to solve for mass, you need to divide a vector by a vector, how!?!?


    Reply With Quote  
     

  2.  
     

  3. #2  
    Suspended
    Join Date
    Feb 2013
    Posts
    1,774
    Quote Originally Posted by Muon321 View Post
    Can you divide by vectors? If so, how? For instance, in F=ma, F and a are vectors, so to solve for mass, you need to divide a vector by a vector, how!?!?
    No, you cannot.


    Reply With Quote  
     

  4. #3  
    Forum Professor
    Join Date
    Jan 2013
    Posts
    1,771
    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by Muon321 View Post
    Can you divide by vectors? If so, how? For instance, in F=ma, F and a are vectors, so to solve for mass, you need to divide a vector by a vector, how!?!?
    No, you cannot.
    Yes, you can. jocular
    Reply With Quote  
     

  5. #4  
    Moderator Moderator Markus Hanke's Avatar
    Join Date
    Nov 2011
    Location
    Ireland
    Posts
    7,302
    Quote Originally Posted by jocular View Post
    Yes, you can. jocular
    xyzt is right, division by vectors is not defined ( obviously ! ); you can only divide the magnitudes of vectors, i.e. you can relate their "lengths" to each other.
    Howard Roark likes this.
    Reply With Quote  
     

  6. #5  
    Forum Bachelors Degree Kerling's Avatar
    Join Date
    Jul 2012
    Location
    Copenhagen
    Posts
    440
    Division isn't an actually existing operator for vectors. But you can multiply with the inverse vector. However, that would be a transposed vector. And hence not really a vector as the original vector was.
    In the information age ignorance is a choice.
    Reply With Quote  
     

  7. #6  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Actually Kerling, this is wrong.

    A field is defined in abstract algebra as a set set equipped with 2 closed binary operations ( and) each with their own inverses and their own identities.

    A vector space is defined as an abelian group together with an associated scalar field.

    The first condition says that for every element in this group there exists another element such that where one takes to be the identity, defined by

    It is usual for an abelian group to write the group operation as (this is what "abelian" means

    It follows that, if arithmetic addition is our group operation, then and the identity must be the zero by . Notice that "subtraction" is not defined.

    The space of all such abstract group elements becomes a vector space when, for any field and any that

    Notice the quotient is well defined in , BUT

    This does not mean that is, for this would imply that and thus our vector space would be a field, which we do not want
    Reply With Quote  
     

  8. #7  
    Suspended
    Join Date
    May 2013
    Posts
    111
    Quote Originally Posted by Kerling View Post
    Division isn't an actually existing operator for vectors. But you can multiply with the inverse vector. However, that would be a transposed vector. And hence not really a vector as the original vector was.
    This is funny. I said something similar to this in another forum and got flamed for it. Of course part of the flame was because I made the goof of solving it as a = F/m when I really meant to obtain m = F/a. Since you weren't insulted for saying this I guess I should stay here.

    The vector he is referring to doesn't have an inverse but it does have a transpose. There is only a limited class of matrices whose inverse is their transpose. An n-tuple is not one of them.

    However if you did multiply each side by it's transpose then you'd get



    You could then take the positive square root to get F = ma and then solve to obtain m = F/a.
    Reply With Quote  
     

Similar Threads

  1. Could use a little help about vectors
    By Peyo in forum Mathematics
    Replies: 12
    Last Post: April 30th, 2013, 03:54 AM
  2. What Are Vectors ???
    By Xidike in forum Physics
    Replies: 6
    Last Post: October 23rd, 2012, 01:29 PM
  3. Relative velocity -vectors
    By Heinsbergrelatz in forum Mathematics
    Replies: 2
    Last Post: January 19th, 2010, 07:19 AM
  4. Visualising vectors in 4D and beyond!
    By talanum1 in forum Mathematics
    Replies: 2
    Last Post: July 27th, 2008, 08:29 AM
  5. resolving vectors
    By almirza in forum Physics
    Replies: 0
    Last Post: November 24th, 2005, 04:09 PM
Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •