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The resultant of two vector 3p and 2p is r if 1st vector is double then resultant aLso get double find angle between vector

The resultant of two vector 3p and 2p is r if 1st vector is double then resultant aLso get double find angle between vector

Grade:11

1 Answers

Arun
25750 Points
6 years ago
The resultant of two vectors A and B is given as √(A^2 + B^2 + 2ABcosΦ), where Φ is the angle between them (what I 've shown in 'phi ', not 'theta ' but the naming of the angle doesn 't really matter; theta cannot be properly represented here)

Therefore √(9p^2 + 4p^2 + 12p^2.cosΦ) is their resultant C (let)

3p doubled -> 6p; therefore new resultant = √(36p^2 + 4p^2 + 24p^2.cosΦ) = D (let)

Now it 's given that, D = 2C

So, squaring on both sides, 4(13p^2 + 12p^2.cosΦ) = 40p^2 + 24p^2.cosΦ

Equating, and cancelling p^2, cosΦ = -1/2 => Φ = 120 degrees or 2π/3 radians

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