Results 1 to 4 of 4

Math Help - Vector translation question

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    61

    Vector translation question

    If p = 2i-j+3k, q=5i+2j and r=4i+j+k, find a set of numbers f,g and h such that fp +gp +hr = 0. What does this tell you about the translations represented by p,q and r?

    I thought to do this I just need to solve 3 simultaneous equations,
    1. 2f + 5g +4h =0
    2. -f + 2g +h =0
    3. 3f + h =0

    But how as I have no constant value and just solve each variable to be zero.
    The book gives 1,2,-3 (or multiples of) and I can see that this is right but I dont know how to get it.
    Also, what does this tell you about the translations represented by p,q and r??

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,326
    Thanks
    1298
    Quote Originally Posted by woollybull View Post
    If p = 2i-j+3k, q=5i+2j and r=4i+j+k, find a set of numbers f,g and h such that fp +gp +hr = 0. What does this tell you about the translations represented by p,q and r?

    I thought to do this I just need to solve 3 simultaneous equations,
    1. 2f + 5g +4h =0
    2. -f + 2g +h =0
    3. 3f + h =0

    But how as I have no constant value and just solve each variable to be zero.
    The book gives 1,2,-3 (or multiples of) and I can see that this is right but I dont know how to get it.
    Also, what does this tell you about the translations represented by p,q and r??

    Thanks.
    I'm not sure what you mean by these as "translations" but the situation you give is precisely the definition of "independent" set of vectors. Since there are three vectors, in 3 dimensions, the fact that they are independent tells you that they form a basis for R3.

    That means, I guess, that you could use those to translate from any point to any other point.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2008
    Posts
    61
    Thanks.

    It made sense not long after I decided to take a break.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by woollybull View Post
    If p = 2i-j+3k, q=5i+2j and r=4i+j+k, find a set of numbers f,g and h such that fp +gp +hr = 0. What does this tell you about the translations represented by p,q and r?

    I thought to do this I just need to solve 3 simultaneous equations,
    1. 2f + 5g +4h =0
    2. -f + 2g +h =0
    3. 3f + h =0

    But how as I have no constant value and just solve each variable to be zero.
    The book gives 1,2,-3 (or multiples of) and I can see that this is right but I dont know how to get it.
    Also, what does this tell you about the translations represented by p,q and r??

    Thanks.
    According to your result

    3\cdot \vec r - 2\cdot \vec q = \vec p

    That means the vectors \vec p, \vec q, \vec r are not independent and therefore they don't form a base of the \mathbb{R}^3
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Translation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 21st 2010, 12:37 PM
  2. translation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 1st 2009, 06:53 AM
  3. translation
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 28th 2009, 07:48 AM
  4. Translation of the cos-1
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 9th 2008, 04:25 PM
  5. translation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 15th 2007, 12:57 PM

Search Tags


/mathhelpforum @mathhelpforum