Q6 of 76 Page 493

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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