What is the perpendicular distance from point P(2, -3, 4) to the plane 2x - y + 2z - 6 = 0?
Answer and explanation
Correct answer: B. 3
- Step 1: Formula for distance from (x_0, y_0, z_0) to Ax + By + Cz + D = 0 is |Ax_0 + By_0 + Cz_0 + D| / sqrt(A^2 + B^2 + C^2).
- Step 2: Numerator: |2(2) - (-3) + 2(4) - 6| = |4 + 3 + 8 - 6| = |9| = 9.
- Step 3: Denominator: sqrt(2^2 + (-1)^2 + 2^2) = sqrt(4 + 1 + 4) = 3.
- Step 4: Distance = 9 / 3 = 3.
Answer
3.
Why not the others: 5 is an arithmetic error using |15|/3; 9 forgets to divide by the magnitude of the normal vector; 1 computes (9 - 6)/3.
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