1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find vector x and scalar λ

  1. May 8, 2012 #1

    sharks

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Find the vector x and the scalar λ which satisfy the equations
    [tex]x \wedge b = b-λc,\; x.c=-2[/tex]where b = (-2, 1, -1) and c = (1, -2, 2)

    2. Relevant equations
    Vector algebra.


    3. The attempt at a solution
    First, i worked on x.c=-2
    Let vector [itex]x = (x_1, x_2, x_3)[/itex]
    So, i got the first equation: [itex]x_1-2x_2+2x_3=-2[/itex]

    Now, working with: [itex]x \wedge b = b-λc[/itex]
    First, i evaluated the L.H.S. and i found the determinant: [itex](-x_2-x_3)\hat i - (-x_1+2x_3)\hat j +(x_1+2x_2)\hat k[/itex]

    Next, i found the R.H.S. and i equated both sides, and added them up to get the second equation: [itex]2x_1+x_2-3x_3=-2-λ[/itex]

    But how to solve both equations to get x and λ? Maybe i've overlooked something...

    I also tried vector algebra on: [itex]x \wedge b = b-λc[/itex] by first doing scalar multiplication by b and then vector multiplication by b.
    I got: [tex]x=\frac{-λ(b\wedge c)}{(b^2-λbc)}[/tex]

    Well, i think i got it. I had to look closer at my scalar multiplication, which gives:
    [tex]λ=\frac{b^2}{bc}[/tex]
    Then, i just have to use the value of λ to find vector x.
    λ=-1 and then it seems that i messed up as in finding x, i got the denominator = 0.
    Any suggestions?

    EDIT: OK... Instead of scalar and vector multiplication by b, i tried the same steps with c.
    I got λ=-1 and x=(-5/6, 5/6, 1/6)
    Is it correct?
     
    Last edited: May 8, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?