Question

a plane meets the coordinate axes in points A, B, C and (alpha, beta,gama) is the centroid of the triangle ABC. then show that the equation of the plane is x/alpha+y/beta+z/gama=3

Answer 1

A ( a,0,0) , B (0, b,0) and C (0,0, c) are the points on co-ordinate axes and centroid (alpha, beta , gama)
we know according to centroid formula ,
alpha =(a+0+0)/3=a/3
a=3.alpha
im the same way ,
b=3. beta
c=3. gama

we also know equation of plane having x-intercept (a), y-intercept(b) and z-intercept (c) are given ,then
x/a +y/b +z/c=1
now put a , b and c value from above ,
x/3.alpha +y/3.beta +z/3.gama =1

x/alpha +y/beta +z/gama =3