The general equation of the plane that contains the points (1, 0, 4), (−1, 1, −4), and the origin is of the form ax + by + cz = 0. Solve for a, b, and c. (Enter the equation of the plane in terms of x, y, and z.)

The equation of the plane is .

Step-by-step explanation:

An equation of the plane containing the point with normal vector is

The equation of any plane can be expressed as

This is called the standard form of the equation of a plane.

Given the points

Two vectors in the plane are

A normal vector to the plane is

Thus, an equation of the plane is

We can check our results with the graph of the plane.