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June 15th, 2012, 09:09 PM   #1
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Vector Question

Hi, This is my first question.. I might be posting it in the wrong section, in that case please direct me. I took this question from IGCSE Mathematics book.
I got the answer to part a) and b)

Now I am struggling with the difficult part, question c) I could not get it.
Can you please lend a hand. (steps are important)

Code:
ANSWER: c) (1 + SQRT(2))b
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File Type: jpg vector_reg_octagon.jpg (21.0 KB, 893 views)
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June 15th, 2012, 09:40 PM   #2
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Re: Vector Question

We know is parallel to b and in the same direction, we just need the magnitude, which we may find from the Pythagorean theorem.

If we draw line segments from vertices A and H to :

[attachment=0:32yo1y44]octagon.jpg[/attachment:32yo1y44]

The interior angles ? of an n-gon have the value, in radians, found by:

hence for an octagon, we have:

and so, referring to the sketch, we find:



Thus, we have:

and consequently and so:



Now, the magnitude of is:

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June 16th, 2012, 12:28 AM   #3
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Re: Vector Question

Thank you very much for the answer.

The thing is that the radiant is not included in the IGCSE O' Level Syllabus. If it is possible to find the answer without using the radiant it will be great.

and I could not understand the part how you got:

b = sqrt(2c) I think it should be b = sqrt(2c^2)

once again thanks for the help it is very much appreciated.
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June 16th, 2012, 12:45 AM   #4
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Re: Vector Question

radians is equal to . So, using this, you may convert the angular measures from radians to degrees.

And the square root, or radical, only has the two under it...it is not .
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June 16th, 2012, 09:28 AM   #5
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Re: Vector Question

Hello, suood!

Here's a non-Trig approach to MarkFL's solution . . .

Code:
          H   1   A
          * - - - *
         /:       :\
      1 / :       : \ 1
       /  :       :  \
    G * - * - - - * - * B
          P       Q






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June 22nd, 2012, 09:55 PM   #6
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Re: Vector Question

Thank you very much for the support..
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