Question

What is the equation of the plane that contains the triangle shown in the diagram?

2x + 3y + z = 6

2x + 3y + 6z = 12

3x + 2y + 6z = 0

6x + 2y + 3z = 18

Answer 1

the first equation

2x + 3y + 6z = 12

Answer 2

Option A is correct.

`2x + 3y +z = 6`

Explanation:

The intercept form of the equation of plane is given by:

`(x)/(l)+(y)/(m) +(z)/(n) =1` .....[1]

where

l is the intercept of x-axes

m is the intercept of y-axes and

n is the intercept of z-axes respectively;

From the given figure;

we have;

The intercepts of coordinates axes are;

`l = 3`

`m = 2`

`n = 6`

Substitute these values in the equation [1]; we have;

`(x)/(3)+(y)/(2) +(z)/(6) =1`

Taking LCM of 3, 2 and 6 is 6

`2x + 3y +z = 6`

therefore, the equation of plane that contains the triangle as shown in the diagram is,
`2x + 3y +z = 6`