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, \(2x + 3y +z = 6\)
