The distance between the parallel planes 2x -2y + z + 3 = 0 and 4x -4y + 2z + 5 = 0 isa)1/2b)1/3c)1/6d)none of the aboveCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

To find the distance between two parallel planes, we follow the method given below. Method:Find the perpendicular distance of each plane from the origin with proper sign (i.e. do not. lake the mod). Ther. their differeee is the required distance between two parallel planes. Let d. and d, be the distances of the planes
2x -2y + z + 3 =0 ...(i)
and 4x - 4y + 2z + 5 = 0 ...(ii)
from the origin. Then

Answer

To find the distance between two parallel planes, we follow the method given below. Method:Find the perpendicular distance of each plane from the origin with proper sign (i.e. do not. lake the mod). Ther. their differeee is the required distance between two parallel planes. Let d. and d, be the distances of the planes
2x -2y + z + 3 =0 ...(i)
and 4x - 4y + 2z + 5 = 0 ...(ii)
from the origin. Then

Answer

Distance between Parallel Planes
The distance between two parallel planes can be calculated using the formula d = |(c1 - c2) / n|, where c1 and c2 are the constants in the equations of the planes, and n is the normal vector to the planes.

Given Planes
The equations of the given planes are:
1. 2x - 2y + z + 3 = 0
2. 4x - 4y + 2z + 5 = 0

Calculating Normal Vector
To find the normal vector, we can take the coefficients of x, y, and z in the equation of the planes. The normal vector for the given planes is <2, -2,='' 1=''> for the first plane and <4, -4,='' 2=''> for the second plane.

Calculating Distance
Substitute the constants and normal vectors into the formula:
d = |(3 - 5) / √(2^2 + (-2)^2 + 1^2)|
d = 2 / √(4 + 4 + 1)
d = 2 / √9
d = 2 / 3
d = 2/3
Therefore, the distance between the given parallel planes is 2/3 units, which corresponds to option 'C'.

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