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Calculate a vector wich forma an angle alpha with another vector

  1. Jul 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Looks very simple, but I need help.
    I have a 2D vector, v, and I need to calculate a vector wich forms an angle [itex]\alpha[/itex] with it.

    Thank you very much

    2. Relevant equations

    I think that the equations should be, for 2 given vector u and v:
    \dpi{150}%20\vec{v}%20\cdot%20\vec{u}%20=%20|\vec{v}|%20\cdot%20|\vec{u}|%20\cdot%20cos%20\alpha.png

    png.latex?\dpi{150}%20\vec{v}%20\cdot%20\vec{u}%20=%20v_x%20\cdot%20u_x%20+%20v_y%20\cdot%20u_y.png

    thanks
     
    Last edited: Jul 21, 2012
  2. jcsd
  3. Jul 21, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    There are, of course, an infinite number of such vectors- of different lengths as well as on either side of u. If you are given vector [itex]\vec{u}= u_x\vec{i}+ u_y\vec{j}[/itex], taking [itex]\vec{v}= v_x\vec{i}+ v_y\vec{v}[/itex], then we must have, as you say, [itex]v_xu_x+ v_yu_v= \sqrt{u_x^2+ u_y^2}cos(\alpha)[/itex].

    There is no "[itex]\sqrt{v_x^2+ v_y^2}[/itex]" in that because I have decided, for simplicity, to look for a unit vector making angle [itex]\alpha[/itex] with [itex]\vec{u}[/itex]. And, of course, that means that [itex]v_x^2+ v_y^2= 1[/itex].

    Solve those two equations for [itex]u_x[/itex] and [itex]u_y[/itex].
     
  4. Jul 21, 2012 #3
    thanks for the help, HallsofIvy, now I see my error. I wasn't using the second equation
     
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