Sun K.

asked • 05/05/13

Find the perpendicular distance between the parallel planes?

Find the perpendicular distance between the parallel planes z+1=x+2y and 3x+6y-3z=4.

Mick S.

answer (to 6 places) = 0.136083 units

observe that the vector < 1, 2, -1 > is normal to both planes .. observe that the point (1, 0, 0) lies in the first plane

the line passing through this point having direction given by the normal vector above has vector equation r(t) = < 1+t, 2t, -t >  for real t

substitute component functions into the equation of the 2d plane to determine that when t = 1/18, the point (19/18, 1/9, -1/18) lies both on the perpendicular line and in the 2d plane

desired answer is the Euclidean distance between these 2 points

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05/06/13

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