Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

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Use tan α = Q + P c o s θ P s i n θ ​ ⇒ tan 9 0 ∘ = Q + P c o s θ P s i n θ ​ = ∞ ∴ Q + P cos θ = 0 ⇒ P cos θ = − Q R = P 2 + Q 2 + 2 PQ cos θ ​ R = P 2 + Q 2 − 2 Q 2 ​ or R = P 2 − Q 2 ​ = 12 144 = ( P + Q ) ( P − Q ) or P − Q = 144/18 = 8 ∴ P = 13 N and Q = 5 N

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