# Thread: Complicated vectors problem.

1. ## (Solved) Complicated vectors problem.

Hi friends
This is a very hard vector question that even my teacher couldn't anwer!
Attached is the diagram.
The question is as follows:
ABCDEFGH is a regular octagon.
AB = a and AH = b . Express the following vecotrs in terms of a and b:
BG
The answer seems to be more complicated than the question. It is (1+√2)b
This question seems imposible to solve!
But there are many smart people here, so I thought I should give it a try.

Thanks in advance

2. I love the tactics meant for alluring: "very hard question", "my teacher couldn't answer", "impossible to solve", "many smart people".

Anyway, the vector BG is certainly parallel to the vector AH, which is why BG is some constant multiple of AH = b.

Draw the straight line segment from B to G, and draw the vertical line segment from A to the line from B to G, and call the point of intersection for I. It's not hard to convince yourself that AHGI is a parallellogram, so the lenght of IG is the same as the lenght of b. To find the rest of the lenght of BG, you need to find the distance from B to I, but do notice that triangle ABI has one right angle and two angles of both 45 degrees. Therefore AI has the same lenght as a (which is the same as the lenght of b), and by the Pythagorean theorem, you get that the lenght of BI is sqrt(2) times the lenght of b, in total, the vector BG is (1+sqrt(2))b.

3. Originally Posted by HappyJoe
I love the tactics meant for alluring: "very hard question", "my teacher couldn't answer", "impossible to solve", "many smart people". .
hehe you got me
I didn't expect someone to actually be able to answer this question though, especially at such short time. my teacher made me wait 15 minute only to tell me "I don't know!"
I might take a while for me to comprehend your method though......
Thanks

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# octagon and vector

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