When two vectors of magnitudes P and Q are inclined at an angle `theta`, the magnitudes of their resultant is 2P. When the inclination is changed to `180^(@)-theta`, the magnitude of the resultant is halved. Find the ratio of `P` and `Q`.

Options

A. `sqrt(2):sqrt(3)`
B. `1: sqrt(3)`
C. `1:sqrt(2)`
D. `sqrt(3):sqrt(2)`

Answer

A

Explanation

`R_(1)^(2)=(2P)^(2)= P^(2)+Q^(2)+2PQ cos theta`
`(P)^(2)= P^(2)+Q^(2)-2PQ cos theta`
Adding them `5P^(2)= 2P^(2)+2Q^(2)`
or `3P^(2)= 2Q^(2)implies P/Q= (sqrt(2))/(sqrt(3))`