Q31 of 34 Page 11

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is [CBSE 2017]

Intercept form of plane is



Now distance of plane (1) from (0,0,0) is-





squaring both sides-



Now for the locus of the centroid we must have


x = (a/3), y = (b/3) & z = (c/3)


⇒ a = 3x, b = 3y & c = 3z


∴ equation (2) becomes






Hence Proved.

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