Q. 75.0( 2 Votes )

A plane meets the

Answer :

Given :


X-intercept = A


Y-intercept = B


Z-intercept = C


Centroid of ∆ABC = (1, -2, 3)


To Find : Equation of a plane


Formulae :


1) Centroid Formula :


For ∆ABC if co-ordinates of A, B & C are


A = (x1, x2, x3)


B = (y1, y2, y3)


C = (z1, z2, z3)


Then co-ordinates of the centroid of ∆ABC are



2) Equation of plane :


Equation of the plane making a, b & c intercepts with X, Y & Z axes respectively is



As the plane makes intercepts at points A, B & C on X, Y & Z axes respectively, let co-ordinates of A, B, C be


A = (a, 0, 0)


B = (0, b, 0)


C = (0, 0, c)


By centroid formula,


The centroid of ∆ABC is given by




But, Centroid of ∆ABC = (1, -2, 3) …… given



Therefore, a = 3, b = - 6, c = 9


Therefore,


X-intercept = a = 3


Y-intercept = b = - 6


Z-intercept = c = 9


Therefore, equation of required plane is




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