If the angle between the lines given by x^2-3 x y+ y^2+3 x-5 y+2=0 ; 0 is ⁻¹ ( 1 3 ) , then the value of is

Step-by-step solution

Given equation of pair of lines is aligned & x^2-3 x y+ y^2+3 x-5 y+2=0 & Here, a =1, ~b = , c =2, f = -5 2 , ~g = 3 2 , ~h = -3 2 & = ⁻¹ ( 1 3 ) = 1 3 aligned Since = | 2 h ^2-a b a + b | aligned & 1 3 = | 2 ( -3 2 )^2- +1 | & ( +1)^2=9(9-4 ) ^2+38 -80=0 & ( +40)( -2)=0 =2 [ 0] aligned