Two equal forces have the square of their resultant equal to three tim

1.	Two equal forces have the square of their resultant equal to three times their product. Find the angle between them.
Answer» Given two forcesPandQ, such that \|P \| =P,\| Q \| =Q, and P = Q, acting at a point, such that square of magnitude R of resultantRofPandQis 3 P² = 3 Q². We are required to find the angle betweenPandQ. Let the angle betweenPandQ is ∅.Then by parallelogram law of vectors we have for the resultant,that, R² = P² + Q² + 2 P Q Cos ∅ = P² + P² + 2 P P Cos ∅= 2 P² + 2 P² Cos ∅. ……..(1) We are given that R² = 3 P². Substituting for R²in equation 1, we get, 3 P² = 2 P² + 2 P² Cos ∅, or Cos ∅ = ½ or ∅ = 60° . The angle between the two forces is 60° .

Two equal forces have the square of their resultant equal to three times their product. Find the angle between them.

Answer»

Given two forcesPandQ, such that |P | =P,| Q | =Q, and P = Q, acting at a point, such that square of magnitude R of resultantRofPandQis 3 P² = 3 Q². We are required to find the angle betweenPandQ.

Let the angle betweenPandQ is ∅.Then by parallelogram law of vectors we have for the resultant,that,

R² = P² + Q² + 2 P Q Cos ∅ = P² + P² + 2 P P Cos ∅= 2 P² + 2 P² Cos ∅. ……..(1)

We are given that R² = 3 P². Substituting for R²in equation 1, we get,

3 P² = 2 P² + 2 P² Cos ∅, or Cos ∅ = ½ or ∅ = 60° .

The angle between the two forces is 60° .

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