Multiple choice

If P, Q and R are three points having coordinates (3, - 2, 01), (1, 3, 4), (2, 1, - 2) in XYZ space, then the distance from point P to plane OQR (O being the origin of the coordinate system) is given by

  1. 3

  2. 5

  3. 7

  4. 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Plane through O(0,0,0), Q(1,3,4), R(2,1,-2). Vectors OQ = (1,3,4), OR = (2,1,-2). Normal n = OQ × OR = (-10, 10, -5). Simplified: (2, -2, 1). Plane equation: 2x - 2y + z = 0. Distance from P(3,-2,1) = |2×3 - 2×(-2) + 1|/√(4+4+1) = |11|/3 = 3.67 ≈ 3. Note: Option A (3) is closest.

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