Results 1 to 10 of 10

Math Help - Vectors, find point to make three points a rectangle

  1. #1
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84

    Exclamation Vectors, find point to make three points a rectangle

    I really could do with some help on 9.b
    Thanks

    http://img7.imageshack.us/img7/5531/scan0004r.jpg
    apolygise is image/link doesn't work, am posting this at school and imageshack is filtered, so I can't check...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    9b. N = 3i + 4j + \left( {c - 3} \right)k.
    Sides must be parallel and equal in length.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84
    Ah I see, so the vector LM has to be the same as ON?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    Quote Originally Posted by LHS View Post
    Ah I see, so the vector LM has to be the same as ON?
    Did you find c is part (a)?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84
    Yes, C=5, and now we have point N part c should be very simple, thank you for your help!
    I kept trying to have ON and MN dotted = to zero to create simultaneous equations, with equations for the line MN's length equalling the length of OL.
    It failed quite superbly, I greatly over complicated matters, would have been useful to know how many marks this question was.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by LHS View Post
    I really could do with some help on 9.b
    Thanks

    http://img7.imageshack.us/img7/5531/scan0004r.jpg
    apolygise is image/link doesn't work, am posting this at school and imageshack is filtered, so I can't check...
    If I didn't misread the question completely then the vectors \overrightarrow{OL} and \overrightarrow{OM} must be perpendicular. Therefore:

    (2,-3,3) \cdot (5,1,c) = 0~\implies~c=-\dfrac73

    The position vector of N is:

    \overrightarrow{ON} = \overrightarrow{OL} + \overrightarrow{OM} = \left(7,-2,\frac23 \right)

    The equation of the line is then:

    \vec r = \overrightarrow{OM} + t \cdot (\overrightarrow{ON} - \overrightarrow{OM})

    Plug in the vectors you know to get the equation of the line.
    Attached Thumbnails Attached Thumbnails Vectors, find point to make three points a rectangle-rechteckimraum.png  
    Follow Math Help Forum on Facebook and Google+

  7. #7
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84
    I'm pretty sure that the lines LM and OL are perpendicular.
    (3i 4j (c-3)k).(2i -3j 3k)=0
    6-12+3c-9=0
    3c=15
    c=5
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    Quote Originally Posted by earboth View Post
    If I didn't misread the question completely then the vectors  \color{red}\overrightarrow{OL} and \color{red}\overrightarrow{OM} must be perpendicular.
    Due to the order of the vertices OLMN we would have \overrightarrow{OL} and \overrightarrow{LM} must be perpendicular.
    Therefore: (2,-3,3) \cdot (3,4,c-3) = 0
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by LHS View Post
    I'm pretty sure that the lines LM and OL are perpendicular.
    (3i 4j (c-3)k).(2i -3j 3k)=0
    6-12+3c-9=0
    3c=15
    c=5
    If the points are in clockwise order then you are right. Sorry for the confusion
    Follow Math Help Forum on Facebook and Google+

  10. #10
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84
    Don't worry about it, we all make mistakes! Thanks for helping though!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find vectors T, N, and B at the given point
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 17th 2009, 07:46 PM
  2. Find the distances of the point using vectors
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 23rd 2009, 08:19 PM
  3. Replies: 1
    Last Post: September 8th 2009, 05:34 PM
  4. find vectors T, N, and B at the given point
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 5th 2008, 09:07 PM
  5. Find point M (vectors)
    Posted in the Geometry Forum
    Replies: 6
    Last Post: March 31st 2007, 03:50 AM

Search Tags


/mathhelpforum @mathhelpforum