Question

Solve this with full explanation!


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Answer 1

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Let take the angle between P and Q is θ.

The force expression according to given conditions are given as,P 2 +Q 2+2PQcosθ=R (1)When Q is doubled,P +4Q 2 +4PQcosθ=4R 2 (2)When Q is reversed,P 2 +Q 2−2PQcosθ=4R 2 (3)Subtracting equation (3) from equation (1), we get4PQcosθ=−3R 2PQcosθ= 4−3R 2

(4)Substituting the value from equation (4) to equation (1), (2) and (3), we get P 2 +Q 2 = 25 R 2P 2 +4Q 2 =7R 2P 2 +Q 2 = 25 R 2

Simplify the above equations, we get P 2=R 2Q 2 = 23 R 2

Thus, the ratio is P:Q:R= 2 : 3 : 2

Answer 2

Answer:

ANSWER

Let take the angle between P and Q is θ.

The force expression according to given conditions are given as,P 2 +Q 2+2PQcosθ=R (1)When Q is doubled,P +4Q 2 +4PQcosθ=4R 2 (2)When Q is reversed,P 2 +Q 2−2PQcosθ=4R 2 (3)Subtracting equation (3) from equation (1), we get4PQcosθ=−3R 2PQcosθ= 4−3R 2

(4)Substituting the value from equation (4) to equation (1), (2) and (3), we get P 2 +Q 2 = 25 R 2P 2 +4Q 2 =7R 2P 2 +Q 2 = 25 R 2

Simplify the above equations, we get P 2=R 2Q 2 = 23 R 2

Thus, the ratio is P:Q:R= 2 : 3 : 2