Question

A plane meets the coordinate axes at A,B,C . So that the centroid of ∆ABC is (1,2,3) then the equation of the plane is ?
Write detailed explanation.​

Answer 1

SOLUTION:-

Let the equation of the plane be,

$= > \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1...............(1)$

The plane meets the coordinate axes at A,B & C.

Hence, we have

A(a,0,0)

B(0,b,0)

C(0,0,c).

Since centroid of ∆ABC is (p,q,r):

Therefore,

$p = \frac{a + 0 + 0}{3} \\ \\ = > a = 3p \\ \\ q = \frac{ 0 + b + 0}{3} \\ \\ = > b = 3q \\ \\ r = \frac{0 + 0 + c}{3} \\ \\ = > c = 3r$

Put in equation (1).

Therefore,

$= > \frac{x}{p} + \frac{y}{q} + \frac{z}{r} = 3$

is the equation of the required plane.

Hope it helps ☺️

Answer 2

Answer:

SOLUTION:-

Let the equation of the plane be,

The plane meets the coordinate axes at A,B & C.

Hence, we have

A(a,0,0)

B(0,b,0)

C(0,0,c).

Since centroid of ∆ABC is (p,q,r):

Therefore,

Put in equation (1).

Therefore,

is the equation of the required plane

Read more on Brainly.in - https://brainly.in/question/11920912#readmoretep-by-step explanation: