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 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`