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Two vectors

  1. Jul 30, 2009 #1
    Two particles move through space in a way that at time t, they are traveling in directions

    (t-6,-t,6) And (1,2,1-t)
    at what time are their directions parallel?

    -

    I know that for them to be parallel, a = Kb, where a and b are the two vectors, and one vector is a scalar of the other

    I get something along the lines of

    (t-6,-t,6) = K(1,2,1-t)
    giving me equations
    t-6 = k
    -t = 2k
    6 = k(1-t)

    please someone check

    I had -t = 2k
    (-t/2) = k

    subbing into t-6

    t-6 = (-t/2)
    2(t-6) = -t
    2t - 12 = -t
    3t = 12
    12/3 = t
    t=4

    is this right?
     
  2. jcsd
  3. Jul 30, 2009 #2

    Mark44

    Staff: Mentor

    This is easy to check. Substitute t = 4 into your two vectors. If this value of t is correct, one vector will be a scalar multiple of the other (and vice versa, but the scalar multiple in this case will be the reciprocal of the other).
     
  4. Jul 30, 2009 #3
    so it's right?
     
  5. Jul 30, 2009 #4

    Mark44

    Staff: Mentor

    What does your check show?
     
  6. Jul 30, 2009 #5
    (-2,-4,6)=k(1,2,-3)

    -2=k*1, k = -2
    -4=k*2 k = -4/2 = -2
    6=k*(-3) k = 6/(-3) = -2

    so yeah

    awesome sauce
    cheers bigears
     
  7. Jul 30, 2009 #6

    Mark44

    Staff: Mentor

    Good work! And you did it all yourself!
     
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