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Q.

If O (origin) is a point inside the triangle PQR such that OP¯+k1OQ¯+k2OR¯=0¯ where k1and k2 are constants such that Area  of triangle PQRArea of triangle OQR=4 then the positive value of k1+k2=______

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answer is 3.

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Detailed Solution

Given that
 a+k1b+k2c=0             Now,Area  of(ΔOQR)Area  of(ΔPQR)=12(ba)×(ca)12|(b×c)|=4
Question Image
 a×b+b×c+c×ab×c=41+k1+k2=4Hence    k1+k2=3
 

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