Two forces are such that the sum of their magnitudes is 18 N, the resultant is 228 N when they are at 120o. Then the magnitude of the forces are

R=P2+Q2+2PQcos⁡θ228=P2+Q2+2(PQ)cos⁡1200228 = P2 + Q2 - PQ........(1)P + Q = 18........(2)From (1) and (2) P =16N, Q = 2N

Two forces are such that the sum of their magnitudes is 18 N, the resultant is 228 N when they are at 120o. Then the magnitude of the forces are

R=P2+Q2+2PQcos⁡θ228=P2+Q2+2(PQ)cos⁡1200228 = P2 + Q2 - PQ........(1)P + Q = 18........(2)From (1) and (2) P =16N, Q = 2N

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Two forces are such that the sum of their magnitudes is 18 N, the resultant is $\sqrt{228}$ N when they are at 120^o. Then the magnitude of the forces are

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12 N, 6 N

13 N, 5 N

10 N, 9 N

16 N, 2 N

answer is D.

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$\begin{array}{l} R = \sqrt{P^{2} + Q^{2} + 2 PQcos θ} \\ \sqrt{228} = \sqrt{P^{2} + Q^{2} + 2 (PQ) \cos 120^{0}} \end{array}$
228 = P² + Q² - PQ........(1)
P + Q = 18........(2)
From (1) and (2)

P =16N, Q = 2N

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Two forces are such that the sum of their magnitudes is 18 N, the resultant is 228 N when they are at 120o. Then the magnitude of the forces are

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Two forces are such that the sum of their magnitudes is 18 N, the resultant is $\sqrt{228}$ N when they are at 120^o. Then the magnitude of the forces are