Results 1 to 4 of 4

Thread: scalar equation of a line -> parametric

  1. #1
    Member
    Joined
    Feb 2008
    Posts
    97

    scalar equation of a line -> parametric

    The question is to find the direction cosines & angles of each line, but one of them is in scalar form, like this:

    3x + 5y + 2 = 0

    How can I find the direction of the vector of the line from scalar form? Or, how can I get this into vector form?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by theowne View Post
    The question is to find the direction cosines & angles of each line, but one of them is in scalar form, like this:

    3x + 5y + 2 = 0

    How can I find the direction of the vector of the line from scalar form? Or, how can I get this into vector form?
    Draw the line. A vector in the direction of the line should now be obvious ......
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    Quote Originally Posted by theowne View Post
    The question is to find the direction cosines & angles of each line, but one of them is in scalar form, like this:

    3x + 5y + 2 = 0

    How can I find the direction of the vector of the line from scalar form? Or, how can I get this into vector form?
    Rewrite the equation:

    $\displaystyle 3x+5y +2 = 0 ~\implies~\langle 3,5 \rangle \cdot \langle x,y \rangle + 2 = 0$

    $\displaystyle \vec n = \langle 3,5 \rangle$ is the normal vector of the line.

    You get the direction vector of the line if you change the order of the components and change the sign at one component:

    The direction vector is now: $\displaystyle \vec d = \langle 5,-3 \rangle$ or $\displaystyle \vec d = \langle -5,3 \rangle$

    Remark: This procedure works only in 2D.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    Quote Originally Posted by theowne View Post
    ...

    3x + 5y + 2 = 0

    ... how can I get this into vector form?
    Change this equation into parametric form:

    $\displaystyle \left| \begin{array}{l}x =0+ t \\y = -2 - \frac35 t\end{array}\right.$

    Now you can rewrite this form into an equation in vector form:

    $\displaystyle \langle x,y \rangle = \langle 0,-2 \rangle + t \cdot \langle 1~,~-\frac35 \rangle$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. parametric equation of line.
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: Oct 15th 2011, 11:00 AM
  2. Parametric Equation for a Line
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jun 6th 2010, 12:59 PM
  3. Replies: 0
    Last Post: Apr 25th 2010, 06:53 PM
  4. Scalar Equation of a line in a Plane
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Oct 14th 2007, 08:55 AM
  5. parametric equation of line
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Dec 16th 2006, 04:39 AM

Search Tags


/mathhelpforum @mathhelpforum