Results 1 to 6 of 6

Math Help - vectors problem

  1. #1
    Junior Member
    Joined
    Dec 2006
    Posts
    28

    vectors problem

    i know that the definition of a unit vector is one such that if you square all the vectors, add them together, and take the square root, you get 1.

    i also know that in order for a vector to be perpendicular to another, the dot product of the two vectors has to equal 0.

    however, i am having trouble finding a unit vector that is perpendicular to the vector (1, -2, 3) so any help would be appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1
    First, I think that you have very confused ideas.
    A unit vector is a vector of length one.
    The length of a vector is the square root of the sum of the squares of its components. Another way: it is the square root of the dot product of the vector with itself.

    To convert a vector to an equivalent( parallel) unit vector simply divide each component of the vector by the length of the vector.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2006
    Posts
    28
    Thanks, but what do you do if you are trying to find a perpendicular vector?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1
    Two vectors are perpendicular if their dot product is zero.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by faure72 View Post
    i know that the definition of a unit vector is one such that if you square all the vectors, add them together, and take the square root, you get 1.

    i also know that in order for a vector to be perpendicular to another, the dot product of the two vectors has to equal 0.

    however, i am having trouble finding a unit vector that is perpendicular to the vector (1, -2, 3) so any help would be appreciated!
    <1, 5, 3>; the unit vector, then, is:

    sqrt(1^2 + 5^2 + 3^2) = sqrt(35)

    <1/sqrt(35), 5/sqrt(35), 3/sqrt(35)>
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,803
    Thanks
    694
    Hello, faure72!

    i am having trouble finding a unit vector that is perpendicular to the vector (1, -2, 3)
    Let v = (a,b,c) be perpendicular to (1,-2,3)

    Then: .(a,b,c)(1,-2,3) .= .0

    And we have: .a - 2b + 3c .= .0

    Obviously, there is no unique answer,
    . . so select any set of numbers that satisfy the equation.

    For example: .(2,1,0)

    Now convert it to a unit vector.
    . . . . . . . . . . . . . . ___________ - - - _
    Its magnitude is: .√2 + 1 + 0 .= .√5
    . . . . . . . . . . . . . . . . . . . . . . _ . . . _
    Divide by the magnitude: . (2/√5, 1/√5, 0) . . . . there!

    [Note: This is but one of a brizillion possible perpendicular vectors.]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vectors problem.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 2nd 2011, 03:58 PM
  2. Vectors problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: August 14th 2010, 04:33 AM
  3. Vectors (Perpendicular vectors) problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 30th 2010, 09:45 AM
  4. Vectors problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 29th 2010, 06:01 AM
  5. Vectors Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 11th 2008, 02:55 PM

Search Tags


/mathhelpforum @mathhelpforum