Find the distance between the two parallel planes 2x - y + 2z = 4 and 2x - y + 2z = 13.
Answer and explanation
Correct answer: B. 3
- Step 1: The distance between parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is d = |D2 - D1| / sqrt(A^2 + B^2 + C^2).
- Step 2: d = |13 - 4| / sqrt(2^2 + (-1)^2 + 2^2) = 9 / sqrt(4 + 1 + 4) = 9 / sqrt(9) = 9 / 3 = 3.
Answer
3.
Why not the others: '9' neglects the normal vector magnitude divisor; '1' calculates (13 - 4) / 9; '9/sqrt(5)' omits one of the squared components.
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