Question

2. The general equation of a plane is Ax + By + Cz = D, where A, B, C, and D are real numbers and A is nonnegative. Find the equation of the plane containing the points (3, 0, 0), (0, 8, 0), and (0, 0, 6). Show each step of your process. Then graph the plane.

I really need a good grade:)

Answer 1

Work this problem as 3 equations and 3 unknowns:

Rewrite the standard equation like this: A/Dx + B/Dy + C/Dz = 1
To clean this up I used new variables: A/D = m, B/D = n, and C/D = o
So: mx + ny + oz = 1
Now put each point onto this equation:
3m + 0 + 0 = 1
0 + 8n + 0 =1
0 + 0 + 6o = 1

In this case you can solve each directly, otherwise you could use substitution.

m = 1/3
n = 1/8
o = 1/6

Put these values in the cleaned up equation:

1/3 x + 1/8 y + 1/6 z = 1

This is in standard form, however you can multiply each term by 24 to remove fractions:

8x + 3y + 4z = 24.