Question

Find the equations ofthe planes that passes through three points.

(a) (1, 1, −1),(6, 4, −5), (−4, −2, 3)

(b) (1, 1, 0), (1, 2,1), (−2, 2, −1)

Answer 1

(a) The givenpoints are A (1, 1, −1), B (6, 4, −5), and C (−4,−2, 3).

Since A, B, C are collinear points, there will be infinite number ofplanes passing through the given points.

(b) The givenpoints are A (1, 1, 0), B (1, 2, 1), and C (−2, 2, −1).

Therefore,a plane will pass through the points A, B, and C.

Itis known that the equation of the plane through the points, ,and ,is

This is the Cartesianequation of the required plane.