Results 1 to 4 of 4

Thread: Sum of a vector parallel to b and a vector orthogonal to b

  1. #1
    Member
    Joined
    Jun 2008
    Posts
    175

    Sum of a vector parallel to b and a vector orthogonal to b

    Vectors are
    $\displaystyle
    \begin{array}{l}
    \underline v = < 2, - 4 > \\
    \underline b = < 1,1 > \\
    \end{array}
    $


    As far as a parallel vector to vector b went it would be just in the same direction and thus for expressing vector v as the sum of a vector parallel to vector b. I thought it would be
    $\displaystyle
    \underline v + \underline b = \left\langle {(2 + 1)} \right.,\left. {( - 4 + 1)} \right\rangle = \left\langle 3 \right.,\left. { - 3} \right\rangle
    $

    and for expressing the vector v as the sum of a vector orthogonal to vector b would be just
    $\displaystyle
    \bot \underline {b = \left\langle { - 1,\left. 1 \right\rangle } \right.}
    $
    and so
    $\displaystyle
    \underline v + \bot \underline b = \left\langle {(2 + ( - 1)),\left. {( - 4 + 1)} \right\rangle = \left\langle {1,\left. { - 3} \right\rangle } \right.} \right.
    $

    However the answer given for the orthogonal part of the question is $\displaystyle
    \left\langle { - 1,\left. { - 1} \right\rangle } \right.
    $
    I'm not sure what I have done wrong in the later part of the question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    5
    Quote Originally Posted by Craka View Post
    Vectors are
    $\displaystyle
    \begin{array}{l}
    \underline v = < 2, - 4 > \\
    \underline b = < 1,1 > \\
    \end{array}
    $


    As far as a parallel vector to vector b went it would be just in the same direction and thus for expressing vector v as the sum of a vector parallel to vector b. I thought it would be
    $\displaystyle
    \underline v + \underline b = \left\langle {(2 + 1)} \right.,\left. {( - 4 + 1)} \right\rangle = \left\langle 3 \right.,\left. { - 3} \right\rangle
    $

    and for expressing the vector v as the sum of a vector orthogonal to vector b would be just
    $\displaystyle
    \bot \underline {b = \left\langle { - 1,\left. 1 \right\rangle } \right.}
    $
    and so
    $\displaystyle
    \underline v + \bot \underline b = \left\langle {(2 + ( - 1)),\left. {( - 4 + 1)} \right\rangle = \left\langle {1,\left. { - 3} \right\rangle } \right.} \right.
    $

    However the answer given for the orthogonal part of the question is $\displaystyle
    \left\langle { - 1,\left. { - 1} \right\rangle } \right.
    $
    I'm not sure what I have done wrong in the later part of the question.
    please state the question as it appears in your book

    am i to understand that you are given vectors v and b and you want to express v as a sum of vectors parallel to b and then as a sum of vectors orthogonal to b?

    if that is the case, why are you adding v to b and v to something parallel to b? it seems that you are not even attempting to do what the problem i think is asking. you want v = (sum of vectors parallel to b) and v = (sum of vectors orthogonal to b) right? how did you end up with v + b on the left side?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2008
    Posts
    175
    Sorry the question states "Let v=<2,4> and b=<1,1>. Express v as the sum of a vector parallel to b and a vector orthogonal to b."
    v and b above are vectors
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    5
    Quote Originally Posted by Craka View Post
    Sorry the question states "Let v=<2,4> and b=<1,1>. Express v as the sum of a vector parallel to b and a vector orthogonal to b."
    v and b above are vectors
    Hint: if $\displaystyle \bold{a}$ is a vector perpendicular to $\displaystyle \bold{b}$, then $\displaystyle \bold{a} \cdot \bold{b} = 0$

    let $\displaystyle \bold{a} = \left< x,y \right>$. then we want $\displaystyle \left< x,y \right> \cdot \left< 1,1 \right> = 0$

    also, any vectors parallel to $\displaystyle \bold{b}$, are of the form $\displaystyle n \bold{b}$. where $\displaystyle n$ is a scalar.

    thus you want to write $\displaystyle \bold{v}$ in the following way

    $\displaystyle \bold{v} = n \bold{b} + m \bold{a}$ for some scalars $\displaystyle m,n$


    i suppose you can continue
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Vector parallel
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 9th 2010, 11:43 PM
  2. parallel vector problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Aug 27th 2010, 01:36 AM
  3. Finding a parallel vector
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Feb 16th 2010, 03:38 AM
  4. Vector parallel to both planes?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Feb 14th 2010, 02:49 AM
  5. Replies: 2
    Last Post: Oct 5th 2009, 04:25 PM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum