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Math Help - experts needed! please! mechanics!

  1. #1
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    Unhappy experts needed! please! mechanics!

    QUESTION ONE:

    i and j represent vectors.

    Given that a= i-2j and b= -3i , find:

    (a) λ, if a + λb is parallel to -i-3j

    (b) μ, if μa + b is parallel to 2i + j



    QUESTION 2:



    The vector a is in the plane of the coordinate axes 0x and 0y as in the above diagram. Find the components of a along 0x and 0y when a equals:

    a) 2
    b) 3
    c) 6
    d) 10




    QUESTION THREE:

    The vector a is in the plane of the coordinate axes 0x and 0y as in the previous question, but makes an angle with the positive direction 0x. Find the components of a along 0x and 0y when a=10 and the angle equals:

    a) 60 degrees
    b) 120 degrees
    c) 150 degrees
    d) 240 degrees
    e) 300 degrees




    QUESTION FOUR:


    Vectors a and b are in the plane of the coordinate axes 0x and 0y, a makes an angle "alpha" with 0x, b makes an angle "beta" with 0x. Find:

    a) the components of a and b along 0x, 0y
    b) the sum of these components along 0x, 0y
    c) the magnitude of a + b
    in each of the following places.

    i) a=3, b=4, alpha=0, beta=90 degrees
    ii) a=3, b=4, alpha=0, beta= 60 degrees
    iii) a=3, b=4, alpha=30 degrees, beta= 60 degrees
    iv) a=5, b=8, alpha=30 degrees, beta=60 degrees
    v) a=5, b=8, alpha=30 degrees. beta=150 degrees




    ANY HELP ON ANY OF THESE QUESTIONS WOULD BE GREATLY APPRECIATED.
    FAIRLY SIMPLE EXPLANATIONS WOULD ALSO BE FABULOUS ! ! !
    THANKSSSS

    EMY.
    XXX
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  2. #2
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    1. Two plane vectors ai + bj and ci + dj are in the same direction the the ratios a:b and c:d are equal. Here a+lb is (1-3l)i - 2j and this is parallel to -i-3j if the ratios (1-3l):-2 and -1:-3 are equal: that is, cross-multiplying, if (1-3l)(-3) = (-1)(-2). So 1-3l = -2/3, l = 5/9.
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  3. #3
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    ok but

    the textbook answer for part (a) is -0.5
    and part (b) is 1

    hmmm

    xx
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  4. #4
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    Try the book answer for yourself: (i-2j) - 0.5(-3i) = 2.5i - 2j. This isn't parallel to -i-3j.
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