Question

The general equation of the plane that contains the points (1, 0, 2), (−1, 1, −2), 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.)

Answer 1

2x-z=0 is the equation of the plane.

Explanation:

Given that the plane passes through the points (1,0,2) and (-1,1,-2)

and also origin.

Hence equation of the plane passing through three points we can use

Any plane passing through 3 given points is given as

`\left[\begin{array}{ccc}x-x_1&y-y_1&z-z_1\\x_2-x_1&y_2-y_1&z_2-z_1\\x_3-x_1&y_3-y_1&z_3-z_1\end{array}\right] =0`

Substitute the three points to get

`\left[\begin{array}{ccc}x-1&y&z-2\\-1-1&1&-2-2\\0-1&0&0-2\end{array}\right] \\=0\\(x-1)(-2) -y(4-4)+(z-2)(1) =0\\-2x+z=0\\2x-z-=0`

2x-z=0 is the equation of the plane.