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, (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3), 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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