The resultant of two forces 3P and 2P is R. If the first force is doubled then resultant is also doubled.The angle between the two forces is

Explanation

`R^(2) = (3P)^(2) + (2P)^(2) + 2 xx 3P xx 2P cos theta` (i)
`(2R)^(2) = (6P)^(2) + (2P)^(2) + 2 xx 6P xx 2P cos theta` (ii)
Dividing (ii) by (i) , we get
`(4)/(1) = ( 40 + 24 cos theta)/( 13 + 12 cos theta)`
`52 + 48 cos theta = 40 + 24 cos theta`
`cos theta = -(1)/(2) rArr theta = 120^(@)`