If a plane meets the coordinate axes at A, B and C in such a way that the centroid of triangle ABC is at the point (1,2,3) then the equation of the plane is

Question

If a plane meets the coordinate axes at A, B and C in such a way that the centroid of triangle ABC is at the point (1,2,3) then the equation of the plane is (A) (x/1)+(y/2)+(z/3)=1 (B) (x/3)+(y/6)+(z/9)=1 (C) (x/1)+(y/2)+(z/3)=(1/3) (D) (x/1)-(y/2)+(z/3)=-1

Tardigrade Admin · Accepted Answer

(1,2,3)=(( a /3), ( b /3), ( c /3)), a =3, b =6, c =9

Q. If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of triangle $A BC$ is at the point $(1, 2, 3)$ then the equation of the plane is

$\frac{x}{1} + \frac{y}{2} + \frac{z}{3} = 1$

$\frac{x}{3} + \frac{y}{6} + \frac{z}{9} = 1$

$\frac{x}{1} + \frac{y}{2} + \frac{z}{3} = \frac{1}{3}$

$\frac{x}{1} - \frac{y}{2} + \frac{z}{3} = - 1$

$(1, 2, 3) = (\frac{a}{3}, \frac{b}{3}, \frac{c}{3}), a = 3, b = 6, c = 9$

Q. If a plane meets the coordinate axes at A,B and C in such a way that the centroid of triangle ABC is at the point (1,2,3) then the equation of the plane is

1x​+2y​+3z​=1

3x​+6y​+9z​=1

1x​+2y​+3z​=31​

1x​−2y​+3z​=−1