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Dear studentI have replaced P1 and P2 by P and QResultant of two forces P and Q is RR = P + Q|R| = sqrt(P2 + Q2 + 2PQCosθ)When Q is doubled new resultant R’ isR’ = P + 2QSince it is perpendicular to P, dot product of R’ and P is zero(R’).(P) = 0(P + 2Q).(P) = 0P^2 + 2PQCosθ = 0(Dot product of P and P is P^2 and that of P and 2Q is 2PQCosθ)Cosθ = -P/(2Q)R = sqrt(P2 + Q2 + 2PQCosθ)R = sqrt(P2 + Q2 + 2PQ*(-P/(2Q))R = sqrt(P2 + Q2 - P2)R = QRegards Arun(askIITians forum expert)
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