How to find Distance between two Planes Please give an example also Thank you - Maths - Three Dimensional Geometry

Question

How to find Distance between two Planes ?

Please give an example also
Thank you

Devesh Kumar · Accepted Answer

There will be 2 kinds of plane:-Intersecting planes and parallel planes If the planes are intersecting, then the distance between them will be 0 So we can find distance between them only when they are parallel Let a1x+b1y+c1z+d1=0 and a1x+b1y+c1z+d2 = 0 are 2 parallel planes Take a point Px1,y1,z1 on any one of these planes and find the length of the perpendicular drawn from Px1,y1,z1 to the other plane The equation of 2 parallel planes is $a x + b y + c z + d_{1} = 0 â¢ â€‰ â€‰; â€‰ â€‰ a x + b y + c z + d_{2} = 0$ distance between the two parallel planes is given by: $d = | \frac{(d_{2} âˆ’ d_{1})}{\sqrt{a^{2} + b^{2} + c^{2}}} |$ let us take the two parallel planes be 2x-y+3z=4 and 2x-y+3z=18 therefore the distance is given by: $d = | \frac{4 âˆ’ 18}{\sqrt{2^{2} + (âˆ’ 1)^{2} + 3^{2}}} | = | \frac{âˆ’ 14}{\sqrt{4 + 1 + 9}} | = | \frac{âˆ’ 14}{\sqrt{14}} | = | âˆ’ \sqrt{14} | = \sqrt{14}$

How to find Distance between two Planes ? Please give an example also . Thank you.