Find equations for the planes in Exercises 21–24. 21. The plane through P0(0, 2, -1) normal to n = 3i - 2j - k 22. The plane through (1, -1, 3) parallel to the plane 3x + y + z = 7 23. The plane through (1, 1, -1), (2, 0, 2), and (0, -2, 1) 24. The plane through (2, 4, 5), (1, 5, 7), and (-1, 6, 8)

Find equations for the planes in Exercises 21–24. 21. The plane through P0(0, 2, -1) normal to n = 3i - 2j - k 22. The plane through (1, -1, 3) parallel to the plane 3x + y + z = 7 23. The plane through (1, 1, -1), (2, 0, 2), and (0, -2, 1) 24. The plane through (2, 4, 5), (1, 5, 7), and (-1, 6, 8)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 19EQ

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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

Find equations for the planes in Exercises 21–24.

21. The plane through P0(0, 2, -1) normal to n = 3i - 2j - k

22. The plane through (1, -1, 3) parallel to the plane 3x + y + z = 7

23. The plane through (1, 1, -1), (2, 0, 2), and (0, -2, 1)

24. The plane through (2, 4, 5), (1, 5, 7), and (-1, 6, 8)

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