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

Options

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

Answer

C

Explanation

`R^(2)=P^(2)+Q^(2)+2PQ cos theta` when `theta`is doubled
`tan90=(2Q sin theta)/(P+2Q cos theta)`