Results 1 to 4 of 4

Thread: Vector Addition Problem

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    79

    Vector Addition Problem

    1. The problem statement, all variables and given/known data

    Write the vector <1,7> as a sum of two vectors, one parallel to <2,-1> and one perpendicular to <2,-1>

    2. Relevant equations
    DOt Product


    3. The attempt at a solution

    I'm confused on where to begin this problem. Should I be using the dot product?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Thanks
    1
    You can do it like this:

    $\displaystyle \displaystyle a \binom{2}{-1} + b \vec{n} = \binom{1}{7}$

    Where $\displaystyle \displaystyle \vec{n} = \binom{x}{y}$

    To find the perpendicular vector n, use the dot product:

    $\displaystyle \displaystyle \binom{2}{-1}\cdot \binom{x}{y} = 0$

    Find a value of x and y that fit in this dot product other than zero. Making a quick sketch will confirm your answer.

    Then, express your answer as the sum of the vectors.

    Post what you get!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,771
    Thanks
    3028
    But you can do it using the dot product.
    The projection of vector $\displaystyle \vec{u}$ on $\displaystyle \vec{v}$ has length $\displaystyle |\vec{u}|cos(\theta)$ where $\displaystyle \theta$ is the angle between the two vectors. It is also true that $\displaystyle \vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta)$ so that the projection of $\displaystyle \vec{u}$ on $\displaystyle \vec{v}$ has length $\displaystyle |\vec{u}|cos(\theta)= \frac{\vec{u}\cdot\vec{v}}{|\vec{v}|}$.

    In order to make that into a vector in the direction of $\displaystyle \vec{v}$ multiply it by the unit vector in the direction of $\displaystyle \vec{v}$:
    $\displaystyle \frac{\vec{v}}{|\vec{v}|}$ to get

    $\displaystyle \frac{\vec{u}\cdot\vec{v}}{|\vec{v}|^2}\vec{v}$

    That is the component of $\displaystyle \vec{u}$ in the direction of $\displaystyle \vec{v}$. To get the conponent perpendicular to that direction, subtract that from $\displaystyle \vec{u}$.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,776
    Thanks
    2823
    Awards
    1
    Here is some different notations.
    Suppose that $\displaystyle U~\&~V$ are two non-parallel vectors.
    Then $\displaystyle U = V_{||} + V_ \bot $ where $\displaystyle V_ \bot = \frac{{U \cdot V}}{{V \cdot V}}V~\&~U_{||} = U - V_ \bot $.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help with applications of vector addition
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Jul 7th 2010, 06:31 PM
  2. Applications of Vector Addition
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Feb 15th 2010, 11:10 AM
  3. Applications of Vector Addition
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Feb 14th 2010, 04:43 PM
  4. addition: magnitude of a vector
    Posted in the Calculus Forum
    Replies: 15
    Last Post: Feb 14th 2009, 08:57 PM
  5. Vector addition
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: Dec 8th 2008, 05:51 AM

Search Tags


/mathhelpforum @mathhelpforum