Given that `P = Q = R` If `vec(P) + vec(Q) = vec(R )` then the angle between `vec(P)` & `vec(R )` is `theta_(1)`. If `vec(P) + vec(Q) + vec(R ) = vec(0)` then the angle between `vec(P)` & `vec(R )` is `theta_(2)`. What is the relation between `theta_(1)` and `theta_(2)` ?

Options

A. `theta_1 = theta_2`
B. `theta_1 = (theta_2)/(2)`
C. `theta_1= 2theta_2`
D. None of the above

Answer

2

Explanation

`vec(Delta r) = vec(OB) - vec(OA)`
`|vec(OA)| = |vec(OB)| =l `
`|vec(Deltar)| = sqrt(l^(2) + l^(2) -2l^(2) cos theta )`
`= sqrt(2l^(2) (1-costheta) ) = sqrt(2l^(2) xx 2sin^(2)theta//2)` ltBrgt `= 2l sin theta//2`