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Math Help - Parallelogram vector problem

  1. #1
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    Parallelogram vector problem

    The parallelogram OABC has it vertices at O (origin) and points A, B and C with poisition vectors a,b and c respectively. The point P is the mid point of AB and the point Q is the midpoint of BC. The line CP meets the line OQ at the point R ( intersection of lines)

    a) write down in terms of a and c, the position vectors b, p and q of the points B, P and Q respectively.

    b) Show that every point on the line CP has a position vector x of the form;

    x=(1-k)a + 1/2(1-k)c where k is any real number

    c) Find thevalue of k in the above formula such that x is a scalar multiple of q
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  2. #2
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    Re: Parallelogram vector problem

    (a), at least, is pretty straight forward. Have you done nothing on this yourself? If you just draw a picture you should see immediately that b= a+ c, p= a+ (1/2), and q= (1/2)a+ c,
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  3. #3
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    Re: Parallelogram vector problem

    Yeah i've completed part (a) but part (b) has got me stumped! Any pointers would be fantastic! Thanks again.
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