Find the position vector of ##Q##

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SUMMARY

The discussion revolves around finding the position vector of point Q in a geometry problem, specifically an O level question. The user initially employed similarity to solve the problem but sought a simpler method for a 2-mark question. The provided solution from the marking scheme was unclear, leading to confusion. The user noted that triangles OPC and QPB are similar with a ratio of 3, and also mentioned that triangle ΔQOA is similar to these triangles.

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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.

1712998784103.png


1712998811995.png



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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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