Consider the plane P, that contains the points A = (1,2, –1), B = (3, 1, 2) and C = (2, – 1, 4). %3D (i) Find the Cartesian equation of the plane P. (ii) Find the distance from the point D = (3, –4, 1) to the plane P.

Consider the plane P, that contains the points A = (1,2, –1), B = (3, 1, 2) and C = (2, – 1, 4). %3D (i) Find the Cartesian equation of the plane P. (ii) Find the distance from the point D = (3, –4, 1) to the plane P.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter7: Conic Sections

Section7.2: Ellipses

Problem 1E: An ellipse is the set of all points in the plane for which the ____ of the distances from two fixed...

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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Consider the plane P, that contains the points A = (1,2, –1), B = (3, 1, 2) and C = (2, – 1, 4).
%3D
(i) Find the Cartesian equation of the plane P.
(ii) Find the distance from the point D = (3, –4, 1) to the plane P.

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