# How To Find The Distance Between Two Planes

This post categorized under Vector and posted on July 13th, 2019.

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31.05.2017 The planes extend out to infinity in all three directions. In the figure we see only a portion of the two planes but its enough to get the idea how the planes cross each other.Autor Gerald LemayAufrufe 37Kgraphiclnge 7 Min.The distance between these two points is 2 and the direction is (100). Now we now that this is not the shortest distance between these two points as (100) neq frac1sqrt6(112) so the direction is not perpendicular to these planes. However this is ok because we can use the dot product between (100) and frac1sqrt6(112) to work out the proportion of the distance that is perpendicular If the distance between the plane Ax-2yz d and the plane containing the lines and they give us two lines here in three-dimensions if that distance is square-root of 6 then the absolute value of d is

Note also that if we have two parallel planes we can calculate the distance between them by subtracting their distances from the origin. Note finally that given a plane and a point its easy to calculate the distance between them by finding the equation of the parallel plane through the point.( 718 65 ) Find the distance between the parallel planes z x 2y 1 and 3x 6y - 3z 4. Solution A point must be found that lies on one of the planes. When y x 0 in the plane z x 2y 1 there exists the point ( 0 0 1 ). To find the distance between the planes we can now use the equation for the distance between a point and a plane.The distance between these two points is 2 and the direction is (100). Now we now that this is not the shortest distance between these two points as (100) neq frac1sqrt6(112) so the direction is not perpendicular to these planes. However this is ok because we can use the dot product between (100) and frac1sqrt6(112) to work out the proportion of the distance that is perpendicular

26.08.2010 1. The problem statement all variables and givenknown data Find the distance between the planes 4x 5y - 3z 4 0 and -8x -10y 6z 12 0.