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$\frac{Px}{(b-c)} = \frac{Qy}{(c-a)} = \frac{Rz}{(a-b)}$

Find the value of $(P*a*x) + (Q*b*y) + (R*c*z)$

This question is a problem of my Class VII textbook and no solved examples of the type are included.

2 Answers2

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HINT:

Set each ratio $=k$

and put the values of $Px$ etc. in $Pax + Qby +Rcz$

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let Px/(b−c)=Qy/(c−a)=Rz/(a−b)= k such that Px = k(b-c), Qy = k (c-a) , Rz = k(a-b) So (P∗a∗x)+(Q∗b∗y)+(R∗c∗z)= kak(b-c) + kbk (c-a) + kc*k(a-b) = 0