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Question:

If the distance between planes 4x - 2y - 4z + 1 = 0 and 4x - 2y - 4z + d = 0 is 7, then d is:

44

41 or 43

41 or 43

42 or 44

Solution:

Distance between two planes 4x - 2y - 4z + 1 = 0 and 4x - 2y - 4z + d = 0 is given by
D = |1 - d| / √(4)² + (-2)² + (-4)²
7 = |1 - d| / 6
1 - d = ±42
d = 43 or -41