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The plane 2x + 3y + 4z =12 meets the coordinate axes in A, B and C. The centroid of ∆ABC is

Given: The plane 2x + 3y + 4z = 12 meets coordinate axes at A, B and C.

To find: Centroid of ∆ABC

Formula Used: Equation of plane is where (x, y, z) is a point on the plane and a, b, c are intercepts on x-axis, y-axis and z-axis respectively.

Centroid of a triangle

Explanation:

Equation of given plane is 2x + 3y + 4z = 12

Dividing by 12,

Therefore the intercepts on x, y and z-axis are 6, 6 and 3 respectively.

So, the vertices of ∆ABC are (6, 0, 0), (0, 4, 0) and (0, 0, 3)

Centroid

= (2, 4/3, 1)

Therefore, the centroid of ∆ABC is (2, 4/3, 1)