Find the position vector of ##Q##

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The discussion focuses on finding the position vector of point Q in a geometry problem, specifically an O level question worth two marks. The original poster used similarity to approach the problem but seeks a clearer or simpler method, suspecting that reflection might be involved. They mention that triangles OPC and QPB are similar with a ratio of 3, and that triangle QOA is also similar to these triangles. The poster is looking for insights or alternative methods to solve the problem effectively. The conversation highlights the challenges of understanding the marking scheme and finding a straightforward solution.
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Homework Statement
see attached (highlighted in Red)
Relevant Equations
vectors
O level question; i used similarity would appreciate an easier approach for 2 marks.

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The ms solution (approach) is not clear to me. Here it is;



1712998905932.png


My approach; using similarity

1712999389794.png


Any insight welcome its a 2 mark question- cannot seem to find easier way though i suspect reflection.
 
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anuttarasammyak said:
View attachment 343313
...still not getting it. You mind giving some reason or thought. Thks.
 
Triangle OPC and QPB are similar with ratio 3.
 
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anuttarasammyak said:
Triangle OPC and QPB are similar with ratio 3.
And ΔQOA is similar to each of those two.
 
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Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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