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Calculate vector with known magnitude along the direciton given by another vector

  1. Nov 8, 2007 #1
    Hi, i have a known magnitude to give my vector in an xy plane, and i have a desired direction. I need the (vx, vy, vz=0) to describe my vector. im sure this can be done easily.

    an example is,

    i have a point at (10,10,0) in cartesian (x,y,z) and will use this as the starting point of my vector. This vector must have a magnitude of 4, and must be in a direction along the line connecting the point (10,10,0) with the origin (0,0,0).

    ie my vector has the magnitude 5 and direciton that of a vector (-10,-10,0).

    in this example the solution is simply to write

    [tex]
    z^{2}=x^{2}+y^{2}[/tex], and as x=y,

    [tex]
    \sqrt{ \frac{z^{2}}{2} }=x=3.5
    [/tex] ish.

    giving me vector with componants (3.5,3.5,0)

    this however is in the wrong direction (need (-3.5,-3.5,0))

    however if x=/=y, how is this solved? and how is the direction accounted for (+ve or -ve)?
     
    Last edited: Nov 8, 2007
  2. jcsd
  3. Nov 8, 2007 #2
    for example a point at (10,9,0) with magnitude 5 along the vector from the point to the origin as before, which is now (-10,-9,0).

    how do i find its componants (vx, vy, vz=0)?
     
  4. Nov 8, 2007 #3
    Find the unit vector first

    First, find the unit vector in your desired direction; then multiply by your desired magnitude.

    The vector (-10, -10, 0) lies on your direction; Now find the unit vector in that direction. i.e. divide by the magnitude. Then multiply by 4.
     
  5. Nov 8, 2007 #4
    excelent, works like a dream. thanks sennyk
     
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