Two forces P and Q , of magnitude 2 F and 3 F , respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is:

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P → = 2 F , Q → = 3 F R → = P 2 + Q 2 + 2 P Q c o s θ = 4 F 2 + 9 F 2 + 12 F 2 c o s θ = F 13 + 12 c o s θ If Q is doubled 2 R → = 4 F 2 + 36 F 2 + 24 F 2 c o s θ = F 40 + 24 c o s θ 4 13 + 12 c o s θ = 40 + 24 c o s θ 12 = - 24 c o s θ c o s θ = - 1 2 θ = 120 °

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