Results 1 to 2 of 2

Thread: parallel vector problem

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    202

    parallel vector problem

    given $\displaystyle \vec{a}=\begin{pmatrix} h-2 \\ 5 \end{pmatrix}$ and $\displaystyle \vec{b}=\begin{pmatrix} 6 \\ 2h \end{pmatrix}$.Find the value of $\displaystyle h$ such that the vector $\displaystyle \vec{a}$ is parallel to the vector $\displaystyle \vec{b}$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    If the vector $\displaystyle \mathbf{a}$ is parallel to vector $\displaystyle \mathbf{b}$, then they have the same direction, and one will be the scalar multiple of another.

    Therefore

    $\displaystyle \mathbf{a} = k\mathbf{b}$

    $\displaystyle \left[\begin{matrix}h-2\\5\end{matrix}\right] = k\left[\begin{matrix}6\\2h\end{matrix}\right]$

    $\displaystyle \left[\begin{matrix}h-2\\5\end{matrix}\right] = \left[\begin{matrix}6k\\2kh\end{matrix}\right]$.


    This means you end up with the system of equations

    $\displaystyle h - 2 = 6k$
    $\displaystyle 5 = 2kh$

    Rearranging the second gives

    $\displaystyle k = \frac{5}{2h}$

    and substituting into the first gives

    $\displaystyle h - 2 = 6\left(\frac{5}{2h}\right)$

    $\displaystyle h - 2 = \frac{15}{h}$

    $\displaystyle h^2 - 2h = 15$

    $\displaystyle h^2 - 2h - 15 = 0$

    $\displaystyle (h - 5)(h + 3) = 0$

    $\displaystyle h = 5$ or $\displaystyle h = -3$.
    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, 10:43 PM
  2. Finding a parallel vector
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Feb 16th 2010, 02:38 AM
  3. Vector parallel to both planes?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Feb 14th 2010, 01:49 AM
  4. Replies: 2
    Last Post: Oct 5th 2009, 03:25 PM
  5. Replies: 3
    Last Post: Oct 15th 2008, 05:21 PM

Search Tags


/mathhelpforum @mathhelpforum