# 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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Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

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