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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