The resultant of two vectors `vec(P)` and `vec(Q)` is `vec(R)`. If `vec(Q)` is doubled then the new resultant vector is perpendicular to `vec(P)`. Then magnitude of `vec(R)` is :-

Options

A. `(P^(2)-Q^(2))/(2PQ)`
B. `Q`
C. `P/Q`
D. `(P+Q)/(P-Q)`

Answer

B

Explanation

`vec(R)=vec(P)+vec(Q), vec(R)'=vec(P)+2vec(Q)`
`:' vec(R)'. vec(P)=0 :. (vec(P)+2vec(Q)).vec(P)=0 rArr P^(2)+2vec(Q).vec(P)=0`
`R^(2)=P^(2)+Q^(2)+2vec(P).vec(Q)=P^(2)+Q^(2)-P^(2)=Q^(2)rArr R=Q`