A plane meets the coordinate axes in A, B, C such that the centroid of the triangle ABC is the point (a, a, a). Then the equation of the plane is x + y + z = p, where p is
A
a
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B
3a
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C
a3
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D
3a
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Solution
The correct option is D3a ∵ Equation of plane x + y + z = p ∴xp+yp+zp=1 ∴ Coordinates of A, B, C are (p, 0, 0), (0, p, 0) and (0, 0, p) respectively. ∵ Centroid of Δ ABC is (a, a, a) ∴a=p3 ⇒p=3a