Q. 9

Mark against the A. (2, 3, 4)

B. (6, 4, 3)

C.

D. None of these

Answer :

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)

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