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Math Help - Vectors

  1. #1
    Member Mr Rayon's Avatar
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    Vectors

    Consider the following relationships between vectors u, v and w.

    i) u = 2v + w
    ii) w = v - u

    Which of the following statements is true?


    A) u = w
    B) u = v

    C) u = \frac{2}{3}v

    D) u = \frac{3}{2}v

    E) u = 3v


    Please explain why to make me understand.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Mr Rayon View Post
    Consider the following relationships between vectors u, v and w.

    i) u = 2v + w
    ii) w = v - u

    Which of the following statements is true?


    A) u = w

    B) u = v

    C) u = \frac{2}{3}v

    D) u = \frac{3}{2}v

    E) u = 3v


    Please explain why to make me understand.
    Note that substituting (ii) into (i) gives us u=2v+v-u\implies 2u=3v\implies u=\tfrac{3}{2}v => (D) is true. Thus, its clear that (B), (C), and (E) are false.

    Note that subsituting (i) into (ii) gives us w=v-\left(2v+w\right)\implies w=-v-w\implies 2w=-v\implies 2w=-\tfrac{2}{3}u\implies 3w=-u, which implies (A) is false.

    Thus, (D) is the only one that is true.
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