Results 1 to 5 of 5

Math Help - Vector equation of a line

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    3

    Vector equation of a line

    I can not find a solution to this question at all, anyone any ideas?

    Find a unit vector that is perpendicular to both 4i + 10j - 3k and 5i - 9j + 7k

    I am as far as finding the vector between them, i - 19j + 10k

    I have called the new vector n1 i + n2 j + n3 k

    Since they are going to be perpendicular n1 -19n2 +10n3 = 0

    I am now stumped.

    Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,386
    Thanks
    1476
    Awards
    1
    If each of U~\&~V are vectors:
    the vector \frac{{U \times V}}{{\left\| {U \times V} \right\|}} is a unit vectot perpendicular to both;

    \arccos \left( {\frac{{U \cdot V}}{{\left\| U \right\|\left\| V \right\|}}} \right) is the angle between them.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2009
    Posts
    3
    I have been told that this method is not on my specification, are there any others?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by r4mbini View Post
    I can not find a solution to this question at all, anyone any ideas?

    Find a unit vector that is perpendicular to both 4i + 10j - 3k and 5i - 9j + 7k

    I am as far as finding the vector between them, i - 19j + 10k

    I have called the new vector n1 i + n2 j + n3 k

    Since they are going to be perpendicular n1 -19n2 +10n3 = 0

    I am now stumped.

    Thanks for your help.
    I cannot follow your solution at all.

    Here is what you need to do:

    (n_1 i + n_2 j + n_3 k) \cdot (5i - 9j + 7k) = 0 \Rightarrow 5 n_1 - 9 n_2 + 7 n_3 = 0 .... (1)

    (n_1 i + n_2 j + n_3 k) \cdot (4i + 10j - 3k) = 0 \Rightarrow 4n_1 + 10n_2 - 3n_3 = 0 .... (2)

    n_1^2 + n_2^2 + n_3^2 = 1 .... (3)

    Solve equations (1), (2) and (3) simultaneously.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2009
    Posts
    3
    I now feel very foolish :P

    Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector equation of a line problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 1st 2011, 10:53 AM
  2. vector equation of a line
    Posted in the Geometry Forum
    Replies: 4
    Last Post: July 2nd 2010, 09:33 AM
  3. tangent line equation from a gradient vector
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 16th 2009, 11:38 AM
  4. Vector equation for the line..
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 8th 2009, 05:01 PM
  5. Replies: 1
    Last Post: October 23rd 2008, 03:39 AM

Search Tags


/mathhelpforum @mathhelpforum