Answer:
Option A is correct.
[tex]2x + 3y +z = 6[/tex]
Step-by-step explanation:
The intercept form of the equation of plane is given by:
[tex]\frac{x}{l}+\frac{y}{m} +\frac{z}{n} =1[/tex] .....[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;
[tex]l = 3[/tex]
[tex]m = 2[/tex]
[tex]n = 6[/tex]
Substitute these values in the equation [1]; we have;
[tex]\frac{x}{3}+\frac{y}{2} +\frac{z}{6} =1[/tex]
Taking LCM of 3, 2 and 6 is 6
[tex]2x + 3y +z = 6[/tex]
therefore, the equation of plane that contains the triangle as shown in the diagram is, [tex]2x + 3y +z = 6[/tex]
