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

Let angle between the vector is `theta` . With the given information we can write the following :
`(y)^(2)=(3x)^(2)+(2x)^(2)+2(3x)(2x) cos theta`
`rArr y^(2)=9x^(2)+4x^(2)+12x^(2) cos theta`
When the first vector is doubled, then resultant is also doubled.
`(2y)^(2)=(6x)^(20)+(2x)^(2)+2(6x)(2x) cos theta`
`rArr 4y^(2)=36x^(2)+4x^(2)+24x^(2) cos theta `
Substituting from equation (1) , we get the following :
`rArr 36x^(2)+16x^(2)+48x^(2) cos theta =36x^(2)+4x^(2)+24x^(2) cos theta`
`rArr cos theta=-(1)/(2)`
`rArr theta=120^(@)`