Forces X,Y and Z have magnitudes `10N 5(sqrt(3)-1) N` and `5(sqrt(3)+1) N`, respectively. The forces Y and Z act in the same direction as shown in (figure) The resultant of X and Y and the resultant of X and Z have the same magnitudes. Find `theta`, the angle between X and Y.

Answer

`150^(@)`

Explanation

Resultant of `vec(X)+vec(Y)=vec(X)+vec(Z)`
`(10)^(2)+(5sqrt(3)-1)^(2))+2.10.(5sqrt(3)-1)cos theta`
`=(10)^(2)+(5sqrt(3)+1)^(2)+2.10.(5sqrt(3)+1)cos theta`
or `(5sqrt(3)-1)^(2)-(5sqrt(3)+1)^(2)=2.10 cos theta[(5sqrt(3)+1)-(5sqrt(3)-1)]`
`(2.5.sqrt(3))(-2)-2.10cos theta[2]=-5/10sqrt(3)=cos theta`
`(-sqrt(3))/2=cos theta rArr theta=150^(@)`