# In ABC, a point P is taken on AB such that AP/BP=1/3 and point Q is taken on BC such that CQ/BQ=3/1 . If R is the point of intersection of the lines AQandCP, ising vedctor method, find the are of ABC if the area of BRC is 1 unitSolution in Tamil

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## Taking A as origin let →band→c be the postion vectors of B and C , respectively, The position vector of Q is 3→b+→c4 and that of p is →b4 ifARQR=λ1 then position vector of R = λ(3→b+→c4) ltbRgt if CRRP=μ1 then position vector of R = μ→b4+→cμ+1 (ii) comparing (i) and (ii) , we have, 3λ4=μ4(μ+1)andλ4=1μ+1 solving , λ=413andμ=12 Therefore, position , vector R is 3→b+→c13 △ABCand△BRC have the same base. there area are proporotional to AQ and RQ △ABC△BRC=∣∣∣3→b+→c4∣∣∣∣∣∣3→b+→c4−(3→b+→c13)∣∣∣=139 Area of △ABC is 13/9 units.

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