Misc 22 - Chapter 11 Class 12 Three Dimensional Geometry

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Misc 22 (Method 1) Distance between the two planes : 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is (A) 2 units (B) 4 units (C) 8 units (D) 2 29 units Distance between two parallel planes Ax + By + Cz = 1 and Ax + By + Cz = 2 is + + So, Distance between the two planes = 4 6 2 2 + 3 2 + 4 2 = 2 4 + 9 + 16 = Hence, (D) is the correct option Misc 22 (Method 2) Distance between the two planes : 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is (A) 2 units (B) 4 units (C) 8 units (D) 2 29 units Distance of a point ( 1 , 1 , 1 ) from the plane Ax + By + Cz = D is + + + + Let us take a point P ( 1 , 1 , 1 ) on the plane 2x + 3y + 4z = 4 2 1 + 3 1 + 4 1 = 4 Now, to find the distance of point P form plane 4x + 6y + 8z = 12, Comparing with Ax + By + Cz = D, A = 4, B = 6, C = 8, D = 12 Distance of P ( 1 , 1 , 1 ) from the plane 4x + 6y + 8z = 12 = 4 1 + 6 1 + 8 1 12 4 2 + 6 2 + 8 2 = 2 + + 12 16 + 36 + 64 = 2 12 116 = 8 12 4 29 = 4 2 29 = Hence, (D) is the correct option