Make it.................

1.	Make it.................
Answer» In 1st case, R2=(3P)2+(2P)2+232P2cosΘ = 9P2+4P2+12P2cosΘ = 13P2+12P2cosΘ ----->(1) In 2ND case, (2R)2=(6P)2+(2P)2+262P2cosΘ ; 4R2=36P2+4P2+24P2cosΘ = 40P2+24P2cosΘ ------->(2) Multiply (1) by 4; 4R2=52P2+48P2cosΘ ------>(3) (3)-(2) gives, 0=12P2+24P2cosΘ Therefore, cosΘ = (-1/2) => Θ = cos-1(-1/2) = 120°

Answer»

In 1st case, R2=(3P)2+(2P)2+2*3*2*P2*cosΘ = 9P2+4P2+12P2cosΘ = 13P2+12P2cosΘ ----->(1)

In 2ND case, (2R)2=(6P)2+(2P)2+2*6*2*P2*cosΘ ; 4R2=36P2+4P2+24P2cosΘ = 40P2+24P2cosΘ ------->(2)

Multiply (1) by 4; 4R2=52P2+48P2cosΘ ------>(3)

(3)-(2) gives, 0=12P2+24P2cosΘ

Therefore, cosΘ = (-1/2) => Θ = cos-1(-1/2) = 120°

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