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

Solution:

We have to find the equation of the plane that contains the triangle.

The intercept form of the equation of plane is given by

\(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\) -------------- (1)

Where, a is the intercept f x-axis

b is the intercept of y-axis

c is the intercept of z-axis

From the given figure,

a = 2

b = 5

c = 4

Put the values of a, b, c in equation (1)

\(\frac{x}{2}+\frac{y}{5}+\frac{z}{4}=1\)

LCM of 2,5,4 is 20

So, \(\frac{10x}{20}+\frac{4y}{20}+\frac{5z}{20}=1\)

10x + 4y + 5z = 20

Therefore, the equation of the plane is 10x + 4y + 5z = 20.

Summary:

The equation of the plane that contains the triangle shown in the diagram is 10x + 4y + 5z = 20.

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