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 magnitudes of the resultant is halved. Find the ratio of `P` and `Q`.

Answer

`sqrt(2)/sqrt(3)`

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)`
or `P/Q=sqrt(2)/sqrt(3)`