`{:("Column- I",,"Column II",),("(Operation of nonzero vectors" vec(P) "and" vec(Q)")",,"(Possivle angle between" vec(P) "and" vec(Q) ")",),((A) |vec(P)xxvec(Q)|=0,,(P)" "90^(@),),((B) |vec(P)xxvec(Q)|=sqrt(3)vec(P).vec(Q),,(Q)" "180^(@),),((C) vec(P)+vec(Q)=vec(R) and P+Q=R,,(R)" "60^(@),),((D)|vec(P)+vec(Q)|=|vec(P)-vec(Q)|,,(S)" "0^(@),),(,,(T)" "30^(@),):}`

Answer

`(A) rarr Q, S; (B) rarr R; (C) rarr S; (D) rarr P`

Explanation

For (A) `|vec(P)xxvec(Q)|=0 rArr` Angle between `vec(P)` & `vec(Q)` is `0^(@)` or `180^(@)`
For (B) `|PQ sin theta|=sqrt(3) PQ cos theta rArr |sin theta|=sqrt(3) cos theta`
Here `cos theta` must be positive so `theta=60^(@)`
For (C) Here `P^(2)+Q^(2)+2PQ cos theta=P^(2)+Q^(2)+2PQ rArr cos theta=1 rArr theta=0^(@)`
For (D) Here `P^(2)+Q^(2)+2PQ cos theta=P^(2)+Q^(2)-2PQ cos theta rArr cos theta=0, rArr theta=90^(@)`