Browse Questions

# The distance between the parallel planes $2x+3y+4z=5\:\:and\:\:4x+6y+8z=12$ is ?

$\begin{array}{1 1} 2 \\ 4 \\ 8 \\ \large\frac{1}{\sqrt {29}} \end{array}$

Toolbox:
• The distance between two parallel planes $ax+by+cz+d_1=0\:\:and\:\:ax+by+cz+d_2=0$ is given by $\bigg| \large\frac{d_1-d_2}{\sqrt {a^2+b^2+c^2}}\bigg|$
$2x+3y+4z-5=0$ is written as $4x+6y+8z-10=0$
( by multiplying by $2$ both the sides )
Then the distance between the planes $4x+6y+8z-10=0\:\:and\:\: 4x+6y+8z-12=0$ is
$\bigg|\large\frac{-10+12}{\sqrt {16+36+64}}\bigg|=\frac{2}{\sqrt {116}}=\frac{1}{\sqrt {29}}$