ABCD is a tetrahedron where A(2,0,0), B(0,4,0) and $CD=\sqrt{14}$ The edge CD lies on the line $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ If locus of centroid of tetrahedron is $\frac{x-\frac{3}{2}}{1}=\frac{y-y_1}{a}=\frac{z-a_1}{b}$ then

$B=2x+3y+4z+1=0.....\left(i\right)$

$x+2y+3z-2=0.......\left(ii\right)$

(iii) is reflection of plane reflection of ax + by + cz + d = 0

$\left(a{a}^1+b{b}^1+c{c}^1\right)\left(a^{1}x+b^{1}y+c^{1}z+d^1\right)$

$=\left(a^{+2}+b^{+2}+c^{+2}\right)(ax+by+cz+d)$

$2(2+6+1)(x+2y+3z-2)$

$=\left(1^2+2^2+3^2\right)(2x+3y+4z+1)$

$4(x+2y+32-2)=14(2x+3y+4z+1)$

$12x + 38y + 64z = 94$

$\Rightarrow 6x+19y+32z=47$