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Math Help - GCSE vectors question

  1. #1
    Member GAdams's Avatar
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    GCSE vectors question

    t = 2a + 3b
    u = 3a - b
    v = a + 2b

    If (t+u+v) is parallel to (4t+kv), find the value of k.

    Thanks.
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  2. #2
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    Hi

    t+u+v = 6a + 4b
    4t+kv = (8+k)a + (12+2k)b

    are parallel if \frac{8+k}{6} = \frac{12+2k}{4}
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  3. #3
    Member GAdams's Avatar
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    Quote Originally Posted by running-gag View Post
    Hi

    t+u+v = 6a + 4b
    4t+kv = (8+k)a + (12+2k)b

    are parallel if \frac{8+k}{6} = \frac{12+2k}{4}
    I can see what you have done but can't see why you have divided
    (8+k)a + (12+2k)b
    by 6a and 4b respectively. Also, not sure why there is an equals sign in the last line.

    Thanks.
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  4. #4
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    t+u+v and 4t+kv being parallel, there exists K such that t+u+v = K(4t+kv)

    This means 6a + 4b = K [(8+k)a + (12+2k)b]

    [6 - K(8+k)]a = [- 4 + K(12+2k)]b

    a and b being independent (or supposed so) this leads to
    6 - K(8+k) = 0 and - 4 + K(12+2k) = 0

    K = 6/(8+k) and K = 4/(12+2k)

    therefore 6/(8+k) = 4/(12+2k)
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