Find the distance between the planes. $$5 x - 2 y + z - 4 = 0,5 x - 2 y + z + 6 = 0$$
A) $\frac { 1 } { 6 }$
B) $\frac { 1 } { 3 } \sqrt { 30 }$
C) $\frac { 5 \sqrt { 30 } } { 6 }$
D) $\frac { 5 } { 6 }$
E) $\sqrt { 30 }$

Question

Quizplus · Accepted Answer

The distance between two parallel planes $Ax + By + Cz + D_1 = 0$ and $Ax + By + Cz + D_2 = 0$ is given by $\frac{|D_2 - D_1|}{\sqrt{A^2 + B^2 + C^2}}$. Here, $A = 5$, $B = -2$, $C = 1$, $D_1 = -4$, and $D_2 = 6$. Thus, the distance is $\frac{|6 - (-4)|}{\sqrt{5^2 + (-2)^2 + 1^2}} = \frac{10}{\sqrt{30}} = \frac{1}{3}\sqrt{30}$.

Find the Distance Between the Planes 5x−2y+z−4=0,5x−2y+z+6=05 x - 2 y + z - 4 = 0,5 x - 2 y + z + 6 = 05x−2y+z−4=0,5x−2y+z+6=0

Find the Distance Between the Planes $5 x - 2 y + z - 4 = 0,5 x - 2 y + z + 6 = 0$