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Help with finding parallel vectors

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    The question states "let u= 2i+mj-10k and v=i-3j+nk, find the value of n and m such that u,v are parallel", the second part states asks the same but "u,v are perpendicular"


    2. Relevant equations



    3. The attempt at a solution
    I attempted to use a dot product solution I guess, because vectors u+v should equal 0 when perpendicular. I'm lost on what to actually do. Thanks in advance.
     
  2. jcsd
  3. Feb 21, 2010 #2
    Remember the definition of the dot product:

    [tex]\vec A \cdot \vec B = A_x B_x + A_y B_y + A_z B_z[/tex]

    As you correctly stated, for two perpendicular vectors, the dot product is 0.

    Let two vectors, [tex]\vec w, \vec q[/tex] be parallel. That means that they're both in the same direction, and therefore, they only differ by some scalar factor R (For instance, [tex]\vec q[/tex] could be 2 times longer than [tex]\vec w[/tex] (R=2) or it could be the same length, but anti-parallel (A negative R value of -1 would achieve that goal) or 2 times longer, but anti-parallel (R=-2)).

    So in general, we can write: [tex]\vec q=R\vec w[/tex]
    Note that we've written a vector equation. That's actually 3 scalar equations in one. Simply solve for your three variables, [tex]R, m, n[/tex] and you're done.

    What's important is that you understand how we've identified parallel\anti-parallel vectors and perpendicular ones. Are these two points clear to you?
     
  4. Feb 21, 2010 #3

    ehild

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    If two vectors

    u=x1 i +y1 j + z1 k and v=x2 i +y2 j + z2 k

    are parallel, then one of them is a multiple of the other

    u=a*v (a is a scalar).

    That means the same for all components:


    x1=a*x2
    y2=a*y2
    z1=a*z2.

    The two vectors are perpendicular if their dot product is 0 which means

    x1x2 + y1y2+ z1z2 = 0.


    ehild
     
  5. Feb 21, 2010 #4
    I somewhat understand what you are saying, so are you saying I need to isolate the unknowns? I still don't fully understand this.
     
  6. Feb 21, 2010 #5
    Yes, solve the linear system of equations.
     
  7. Feb 21, 2010 #6
    Ok, trying this with the perpendicular qustion it'd be "(2i+mj-10k) . (i-3j+nk)=0". I would have 2 unknowns, how would I solve this. I still don't know how to go about the parallel question.
     
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