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The magnitude of two forces P and Q are in the ratio P:Q =1:2 if their tan^-1(3/2) to vector P, then the angle between P and Q is |
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Answer» Answer: The FORMULA for direction of the resultant force is given by = Qsin θ / (P + Q cos θ). In the data, it is given that P and Q are in the ratio 1:2. Also, it is mentioned that the angle is √3/2. By substituting these values into the formula, we get √3/2 = 2sin θ / (1 + 2 cos θ) √3/2 = 2sin θ / (1 + 2 cos θ) Now you can go ahead and solve this EQUATION to find the value of θ. But that will be a TEDIOUS process and demands some time. Therefore, if this is a competitive exam question, I suggest you to use the inspection method INSTEAD. This method involves substituting common values of θ for which the trigonometric ratios are already known. For example, let us substitute θ=60° Then, √3/2 = 2sin 60° / (1 + 2 cos 60°) √3/2 = (2 * √3/2) / (1 + 2 * 1/2) √3/2 = (√3) / (1+1) √3/2 = √3/2 LHS=RHS Hence we conclude that the angle between P and Q is 60° hope it helps u mark me brainliest one |
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