Please explain it with Diagrammatic Representation,

Q. A plane meets the coordinate axes in A, B, C such that the centroid of triangle  ABC is the point (p, q, r). Show that the equation of the plane is   x p + y q + z r   =   3

Dear student
The question is saying:A plane cuts the coordinates axes at A,B,C respectively.Centroid is given as p,q,r.Show  equation of plane isxp+yq+zr=3
Although everything has been explained properly, but still I am providingthe solution.Let the equation of plane be,xa+yb+zc=1  ...1The plane meets the coordinate axes at A,B and C.Hence we haveAa,0,0,B0,b,0,C0,0,cSince centriod of ABC is p,q,rSo, p=a+0+033p=aq=0+b+033q=br=0+0+c33r=cPutting in eq 1So, x3p+y3q+z3r=1xp+yq+zr=3is the required eq. of plane

  • 0
What are you looking for?