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in Mathematics by (70.5k points)

If perpendicular distance from (0, 0, 0) to the variable plane is p and variable plane intersects the axis in A, B, C, the centroid of ΔABC is on (1/x2) + (1/y2) + (1/z2) = ____

(A) (9/p2)

(B) (p2/9)

(C) (p/9)

(D) (9/p)   

1 Answer

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by (71.7k points)
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Best answer

The correct option (A) (9/p2)   

Explanation:

point on axis A(a, 0, 0), B(0, b, 0) and C(0, 0, c)

centroid of ΔABC(x1, y1, z1) = [(a/3), (b/3), (c/3)] A, B, C satisfied plane (x/a) + (y/b) + (z/c) = 1

also distance from (0, 0, 0) to plane is p

∴ p = [1/√{(1/a2) + (1/b2) + (1/c2)}]

∴ (1/p2) = (1/a2) + (1/b2) + (1/c2)

∴ (1/p2) = [1/(9x12)] + [1/(9y12)] + [1/(9z12)]

centroid of ΔABC is on (1/x2) + (1/y2) + (1/z2) = (9/p2).

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