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
Answers
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°
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