A line intersects the coordinate axes at A, B, and C such that the centroid of ΔABC is at (p, q, r). The equation of the plane passing through A, B, and C is: A. x/p + y/q + z/r = 1 B. x/p + y/q + z/r = 3 C. px + qy + rz = 1 D. px + qy + rz = 3 Answer: B) x/p + y/q + z/r = 3 Explanation: Let intercepts be a, b, c. Centroid is (a/3, b/3, c/3) = (p, q, r). So a=3p, b=3q, c=3r. Plane is x/a + y/b + z/c = 1 → x/(3p) + y/(3q) + z/(3r) = 1 → x/p + y/q + z/r = 3.

imo class 12 three dimensional geometry

A line intersects the coordinate axes at A, B, and C such that the centroid of ΔABC is at (p, q, r). The equation of the plane passing through A, B, and C is:

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A line intersects the coordinate axes at A, B, and C such that the centroid of ΔABC is at (p, q, r). The equation of the plane passing through A, B, and C is:

A. x/p + y/q + z/r = 1
B. x/p + y/q + z/r = 3
C. px + qy + rz = 1
D. px + qy + rz = 3

Answer: B) x/p + y/q + z/r = 3

Explanation: Let intercepts be a, b, c. Centroid is (a/3, b/3, c/3) = (p, q, r). So a=3p, b=3q, c=3r. Plane is x/a + y/b + z/c = 1 → x/(3p) + y/(3q) + z/(3r) = 1 → x/p + y/q + z/r = 3.

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