If the system of linear equations. 8 x + y + 4 z = - 2 x + y + z = 0 λ x - 3 y = μ has infinitely many solutions, then the distance of the point λ , μ , - 1 2 from the plane 8 x + y + 4 z + 2 = 0 is:

Step-by-step solution

Given the system of linear equations. 8 x + y + 4 z = - 2 x + y + z = 0 λ x - 3 y = μ has infinitely many solutions, so D = 8 1 4 1 1 1 λ - 3 0 = 0 ⇒ λ = 4 Also D 1 = D 2 = D 3 = 0 D 1 = - 2 1 4 0 1 1 μ - 3 0 = 0 ⇒ - 6 - 3 μ = 0 So μ = - 2 Hence the point will be 4 , - 2 , - 1 2 Now distance of point 4 , - 2 , - 1 2 from plane 8 x + y + 4 z + 2 = 0 = 32 - 2 - 2 + 2 8 2 + 1 2 + 4 2 = 30 9 = 10 3