Find the equations of the planes that passes through three points.

(1, 1, 0), (1, 2, 1), (–2, 2, –1)

The given points are (1, 1, 0), (1, 2, 1), (-2, 2, -1).

Let,

= 1(-2 - 2) – 1(-1 + 2)

= -4 – 1

= -5 ≠ 0

There passes a unique plane from the given 3 points.

Equation of the plane passes through the points, (x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}) and (x_{3}, y_{3}, z_{3}), i.e.,

⇒ (x - 1)(-2) – (y - 1)(3) + 3z = 0

⇒ -2x + 2 – 3y + 3 + 3z = 0

⇒ 2x + 3y – 3z = 5

This is the required eq. of the plane.

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