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

Options

A. `theta_(1)=theta_(2)`
B. `theta_(1)=theta_(2)/2`
C. `theta_(1)=2theta_(2)`
D. None of these

Answer

B

Explanation

`:' vec(P)+vec(Q)=vec(R)" ":. vec(Q)=vec(R)-vec(P)`
`rArr Q^(2)=R^(2)+P^(2)-2RP cos theta_(1)`
`rArr cos theta_(1)=1/2 rArr theta_(1)=pi/3`
Now `:' vec(P)+vec(Q)+vec(R)=vec(0) :. vec(P)+vec(R)=-vec(Q)`
`rArr P^(2) +R^(2)+2PR cos theta_(2)=Q^(2)`
`rArr cos theta_(2)=-1/2 rArr theta_(2)=(2pi)/3`