The correct option is D Both Statement I and Statement II are true.
Given that →P is perpendicular to →Q, hence→P.→Q=0
Using paralellogram law, Resultant formula is given by
R=√|→A|2+|→B|2+2|→A||→B|cosθ
Here→A=(→P+→Q)⟹|→A|=√P2+Q2,(∵→P.→Q=0)
→B=(→P−→Q)⟹|→B|=√P2+Q2 (∵→P.→Q=0)
Hence R=√P2+Q2+P2+Q2+2(P2+Q2)cosθ
R=√2(P2+Q2)(1+cosθ)
(i)If R=√3(P2+Q2), θ=θ1
√3(P2+Q2)=√2(P2+Q2)(1+cosθ1)
3=2(1+cosθ1)
cosθ1=0.5
θ1=60∘
(ii)If R=√2(P2+Q2), θ=θ2
√2(P2+Q2)=√2(P2+Q2)(1+cosθ2)
2=2(1+cosθ2)
cosθ2=0
θ2=90∘
Both Statement I and Statement II are true.