What is the distance between the two parallel planes 2x - y + 2z = 4 and 2x - y + 2z = 13?
Answer and explanation
Correct answer: C. 3 units
- Step 1: Formula for distance between parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2:
- Step 2: d = |D2 - D1| / sqrt(A^2 + B^2 + C^2).
- Step 3: Here D1 = 4, D2 = 13, and normal vector is (2, -1, 2).
- Step 4: Calculate denominator: sqrt((2)^2 + (-1)^2 + (2)^2) = sqrt(4 + 1 + 4) = sqrt(9) = 3.
- Step 5: Calculate numerator: |13 - 4| = 9.
- Step 6: Compute distance: d = 9 / 3 = 3 units.
Answer
3 units.
Why not the others: '9 units' neglects the denominator normal magnitude; '1 unit' divides by 9; '4.5 units' divides by 2.
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