Find the perpendicular distance from point P(1, 2, 3) to the plane 2x - 2y + z + 5 = 0.
Answer and explanation
Correct answer: A. 2
- Step 1: Use plane distance formula: d = |Ax0 + By0 + Cz0 + D| / sqrt(A^2 + B^2 + C^2).
- Step 2: Evaluate numerator: |2(1) - 2(2) + 1(3) + 5| = |2 - 4 + 3 + 5| = |6| = 6.
- Step 3: Evaluate denominator: sqrt(2^2 + (-2)^2 + 1^2) = sqrt(4 + 4 + 1) = sqrt(9) = 3.
- Step 4: Compute quotient: d = 6 / 3 = 2.
Answer
2.
Why not the others: '6' omits dividing by the plane normal vector magnitude; '18' multiplies numerator by denominator; '3' uses the denominator magnitude alone.
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