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Find the shortest distance between the planes?

Find the shortest distance between the planes 2x+3y-z=2 and 2x+3y-z=4.

Comments

2/sqrt(14) = 2sqrt(14)/14 = sqrt(14)/2

Typo!

2/sqrt(14) = 2sqrt(14)/14 = sqrt(14)/7

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1 Answer

Pick any point from the first plane, (0, 0, -2). Using the distance formula from a point to a plane, you can find the shortest distance

d = |-2+4|/sqrt(2^2+3^2+1^2) = 2/sqrt(14).