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JEE Main 2013

JEE Main 2013 Mathematics question on Three Dimensional Geometry

Distance between two parallel planes 2x+y+2z=82x + y + 2z = 8 and 4x+2y+4z+5=04x + 2y + 4z + 5 = 0 is
  1. A.
    32\dfrac{3}{2}
  2. B.
    52\dfrac{5}{2}
  3. C.
    72\dfrac{7}{2}
  4. D.
    92\dfrac{9}{2}
Show answer and solution

Correct option: C

Solution

Rewrite the second plane as 2x + y + 2z + 5/2 = 0. Now both planes are in the form 2x + y + 2z = 8 and 2x + y + 2z = -5/2. Distance = |8 - (-5/2)| / √(4+1+4) = |8 + 5/2| / 3 = (21/2) / 3 = 7/2.

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