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Math Help - Vector/Equation problem

  1. #1
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    Vector/Equation problem

    Three collinear vectors, a, b, and c, are such that a=(2/3)b and a=1/2c.

    Determine integer values for m and n such that mc +nb = 0. How many values are possible for m and n to make this statement true?

    P.S. Variables "a," "b," c," and "0" are vectors.

    I'm a little lost on how you'd solve this.
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  2. #2
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    Quote Originally Posted by IanCarney View Post
    Three collinear vectors, a, b, and c, are such that a=(2/3)b and a=1/2c.
    Determine integer values for m and n such that mc +nb = 0. How many values are possible for m and n to make this statement true?
    Can you show that does in fact work?
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  3. #3
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    Quote Originally Posted by Plato View Post
    Can you show that does in fact work?
    Like this?

    b=(3/2)a and c=2a

    2m+3/2n=0

    4m+3n=0

    The answer in the book is: Answers may vary. For example: m=4, n=-3, infinitely many
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  4. #4
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    Quote Originally Posted by IanCarney View Post
    The answer in the book is: Answers may vary. For example: m=4, n=-3, infinitely many
    That is correct. Any value of m gives a value for n.
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