If the equation of a floor of a room is given by $x+y-z+4=0$ and the equation of roof is given by $x+y-z+5=0$. Then, the height of the room is :

$\frac{1}{\sqrt{3}}$ units

Equation of plane

$P_1 : x + y - z + 4 = 0$

$P_2 : x + y - z + 5 = 0$

for this case

a = 1

b = 1

c = -1

So $d_1 = 4$

$d_2 = 5$

Distance between parallel plain P₁ and P₂

= height of room = $\frac{|d_2-d_1|}{\sqrt{a^2+b^2+c^2}}$

$\Rightarrow \frac{|5-4|}{\sqrt{1^2+1^2+(-1)^2}} = \frac{1}{\sqrt{3}}$