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Vector & Square Root Question for GCSE Maths

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  1. Jun 1, 2014 #1
    I have attached a copy of a vector question which i cannot do, i do not even understand what the question is asking can someone help?

    On a different note i seem to have a lot of trouble with simplifying square roots for example what is the square root of 2704/ is there any way to find the root easily?

    Thanks
     

    Attached Files:

  2. jcsd
  3. Jun 1, 2014 #2
    The vector question:

    Remember that the defining parts of a vector are its length and direction. You can produce a vector of the same length and direction (but not position) as BC using some combination of AB and CD. Hint: How does the distance from A to the midpoint compare to the distance from B to C? What about the angles? Can you prove it?

    The roots question:

    I use a calculator, to be honest. But, in a pinch, I would decompose the number into prime factors like so:

    sqrt(2704) = sqrt(2*2*2*2*13*13) = sqrt(2^4 * 13^2) = 4*13 = 52

    Finding the factors is a bit time consuming though.
     
  4. Jun 1, 2014 #3
    Factor the 2704 into its lowest factors. Start with 2.

    Chet
     
  5. Jun 1, 2014 #4

    tms

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    It's a regular hexagon. What does that tell you about the lengths of the sides?

    How about a calculator? If you want a manual method, you could start here: http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
     
  6. Jun 1, 2014 #5

    haruspex

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    It can be done in the head like this:
    2704 = 2700+4 = 4*(27*25+1) = 4*((26+1)(26-1)+1) = 4*((262-12)+1)...
     
  7. Jun 1, 2014 #6

    tms

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    Of course, the quick and lazy way to factor a number is with a package such as Maxima or GNU Octave:

    Code (Text):
    (%i1) factor(2704);

                                         4   2
    (%o1)                               2  13
     
  8. Jun 1, 2014 #7

    I am trying to prove that the distance from A to the mid point is equal to the midpoint to any other corner, what i have done is found the angles at the midpoint (360/6) to get 60 degrees, i have alos found the interior angles which is 120 degrees and the exterior angles which are 60 degrees but i cannot prove the length of the mid point is equal to the midpoint to all other points?

    see attached.
     

    Attached Files:

  9. Jun 1, 2014 #8
    Would it help to note that the triangles inside are all equiangular, and therefore equilateral? Every side of every triangle has the same length.

    Edit: If we want to prove this rigorously, I would start with the fact that |FC| = 2|AB| (given), therefore |FO| = |AB|. But, I doubt that this is necessary as long as you have a convincing (and correct!) argument.
     
    Last edited: Jun 1, 2014
  10. Jun 1, 2014 #9

    tms

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    The question asks you to relate the length of one side to the lengths of two other sides. Just consider the definition of a regular polygon, and the answer should be obvious.
     
  11. Jun 2, 2014 #10

    verty

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    But let's pretend that it isn't a regular hexagon, this makes the question more interesting. Essentially you must tackle this like a geometry problem, start from what you know and fill in anything you can add with geometric reasoning. Eventually you will find a way forward.
     
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