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Homework Help: A few vector problems

  1. Jan 13, 2005 #1
    ive been struggling with these for an hour and a half.
    they arent hard, i just cant seem to make them work.
    the first one is:
    A = (5,3,2)
    B = (-1,4,6)
    C = (8,2,0)

    im using this format (x,y,z)

    aA+bB+ C = a vector parallel to the y-axis.
    so, that means i need to find a vector with only z components right?
    well, the answers out of the back of the book are a = -12/7 and b = -4/7.
    these dont work out.



    heres the second one
    A = (a,1,4)
    B = (3,b,-6)
    C = (5,-2,c)

    Im supposed to find a,b, and c so that all three vectors are perpendicular to each other.
    that means i should use the dot product with A and B, A and C, and B and C and set the dot product equal to zero for all three. So I did this, and i got answers for a, b and c but they dont work out when i check them.
     
  2. jcsd
  3. Jan 13, 2005 #2
    if a vector is parallel to y axis, that's means the vector is pointing at y direction.... so what will the x and z component of this vector be? after you have the x and z component.. what you ganna to is write down the equation for x&z component... then you will have 2 equation, with 2 unkn..for the 2nd problem, your method is completely fine... check your algebra again
     
  4. Jan 13, 2005 #3
    okay, i tried this
    5a -b + 8 = 1
    3a + 4b +2 = 0
    this leaves a 1 in x, and a 0 in y

    i solved it this way, and got close to the right answer. am i on the right track?
     
  5. Jan 13, 2005 #4
    okay, this way should be right
    5a - b = -8
    2a + 6b = 0
    a = -1.5
    b = .5
    maybe the answers in the back of the book are wrong?
     
  6. Jan 14, 2005 #5
    Hi Formulajoe,

    Did you consider the questions of Vincenchan ?
    If a vector should be parallel to the y axis, what requirements can you put on the x, y, z coördinates. I'm sure you can work out the algebra to calculate the solutions, but I've got the impression you're a bit in the vague as to what you need to calculate...

    Greetz,
    Leo
     
  7. Jan 14, 2005 #6
    Hi formulajoe,

    you're right. Your solution is correct. Maybe the answers in your book are wrong.
     
  8. Jan 14, 2005 #7

    Galileo

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    Homework Helper

    If a = -12/7 and b = -4/7 then the z-component of aA+bB+C is:
    (-12/7)(2)-(4/7)(6)+0=-48/7

    So it is not parallel to the y-axis.
    Check if you read the question correctly. If you did, then the books answer if wrong.
     
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