The frame ACD is hinged at A and D and is supported by a cable that passes through a frictionless ring at B and is attached to hooks at G and H$.$ Knowing that the tension in the cable BG $($TBG$)$ and BH $($TBH$)$ is $450$ N$,($a$)$ determine the vector moment $($N$.$m$)$ about point A of the force exerted on the frame by portion BG of the cable using matrix determinant method $($b$)$ calculate the perpendicular distance $($m$)$ from point A to cable BG$.$