Question

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

Answer 1

The first equation

2x + 3y + 6z = 12

Answer 2

Answer:

Option A is correct.

$2x + 3y +z = 6$

Step-by-step explanation:

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

$\frac{x}{l}+\frac{y}{m} +\frac{z}{n} =1$            .....[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;

$\frac{x}{3}+\frac{y}{2} +\frac{z}{6} =1$  

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, $2x + 3y +z = 6$