(288)

Given,

The plane x + 3y - 2z + 6 = 0 meet the co-ordinate axes at the points A, B, C,

So, A(-6,0,0), B(0, -2,0) & C(0,0,3)

And the orthocenter of the triangle ABC is

We know that, circumcentre of triangle is point of intersection of perpendicular bisectors, So, plotting the diagram we get,

Now from diagram we can see that O to midpoint of BC BC

So, by perpendicular vector formula we get,

.......

Similarly, for side AC we get,

…

Similarly, for side AB we get,

(x + 3)x(-6)+(y + 1)x2 +(z - 0)x0 = 0

3x-y+ 8 = 0.........

Now from equation , & we get,

Now using the relation between centroid, circumcentre and orthocentre, we get,

Now on comparing both side we get,

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