The volume of the cube whose two faces lie on the plane $6x-3y+2z+1=0 $ and $6x-3y+2z+4=0$

708 Views Asked by At

The volume of the cube whose two faces lie on the plane $6x-3y+2z+1=0 $ and $6x-3y+2z+4=0$ is equal to

(a) 27

(b) 27/349

(c) 3/7

(D) 10

My work : the distance between the two plane is$ =\frac{6-3+2+4}{\sqrt{6^2+3^2+2^2}}-\frac{6-3+2+1}{\sqrt{6^2+3^2+2^2}}=\frac{3}{7}$.

So the length of one side is= 3/7 . Hence volume is $=(\frac{3}{7})^3=\frac{27}{343}$ .

Is my work correct ??