Results 1 to 2 of 2

Thread: Vector problem

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    202

    Vector problem

    Givan a=3x+4y and b =(h+5)x-(2k-3)y,find in term of h,k,x and y,vector a-2b.If the vector a-2b is a zero vector and x and y are non-zero vectors,find the values of h and k.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, mastermin346!

    This is quite straight-forward.
    Exactly where is your difficulty?


    Given: .$\displaystyle \begin{array}{ccc}\vec a &= & 3\vec x+4\vec y \\ \vec b &=& (h+5)\vec x -(2k-3)\vec y\end{array}$

    . . find $\displaystyle \vec a-2\vec b$ in terms of $\displaystyle h,k, \vec x,\vec y.$

    $\displaystyle \vec a - 2\vec b \;=\;(3\vec x-4\vec y) - 2\bigg[(h+5)\vec x - (2k-3)\vec y\bigg] $

    . . . . $\displaystyle =\;3\vec x+ 4\vec y - 2(h+5)\vec x + 2(2k-3)\vec y $

    . . . . $\displaystyle =\; 3\vec x + 4\vec y - 2h\vec x - 10\vec x + 4k\vec y - 6\vec y$

    . . . . $\displaystyle =\;-2h\vec x - 7\vec x + 4k\vec y - 2\vec y $

    . . . . $\displaystyle =\;-(2h+7)\vec x + 2(2k-1)\vec y$




    If the vector $\displaystyle a -2b$ is the zero vector and $\displaystyle x$ and $\displaystyle y$ are non-zero vectors,
    . . find the values of $\displaystyle h$ and $\displaystyle k$.

    If $\displaystyle \vec a - 2\vec b \:=\:\vec0$, then: . $\displaystyle \begin{array}{ccccccccc}\text{-}(2h+7) \;=\;0 & \Rightarrow & h \;=\;\text{-}\frac{7}{2} \\ \\[-3mm] 2(2k-1) \;=\;0 & \Rightarrow & k \;=\; \frac{1}{2} \end{array}$

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. vector problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Dec 10th 2011, 10:17 AM
  2. Another Vector Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 10th 2010, 11:18 AM
  3. [SOLVED] Vector Dot Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Oct 18th 2010, 10:25 AM
  4. Vector problem
    Posted in the Geometry Forum
    Replies: 6
    Last Post: Jul 3rd 2009, 06:30 PM
  5. vector problem sum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jan 9th 2009, 08:42 AM

Search Tags


/mathhelpforum @mathhelpforum