How do I calculate the distance between the two parallel planes #x - 2y + 2z = 7# and #2y - x - 2z = 2#?

1 Answer
Rui D.
Jan 4, 2016

Choose a point in any of the planes and calculate the distance between this point and the other plane.
In case #d=3#

Explanation:

If the planes are parallel, any point of one plane is at the same distance to the other plane.

Choosing a point in plane 1, with #y=0# and #z=0#:
#x-2*0+2*0=7# => #x=7# => #P(7,0,0)#

Rearranging equation of second plane:
#-x+2*y-2*z-2=0#

Formula of distance between a point and a plane:
#d=(|a*x_p+b*y_p+c*z_p+d|)/sqrt(a^2+b^2+c^2#
#d=(|(-1)7+2*(0)+(-2)*0-2|)/sqrt((-1)^2+(2)^2+(-2)^2)=(|-7+0+0-2|)/sqrt(1+4+4)=9/3# => #d=3#

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