Explanation Given: The four points in the field are ( 1 , 1 , 2 ) , ( 2 , 3 , 9 ) , ( − 2 , 1 , − 1 ) and ( 1 , 2 , 5 ) . Approach: Using vector algebra and cross product to check whether these points lie on the same plane or not. Calculation: Given that the four points ( 1 , 1 , 2 ) , ( 2 , 3 , 9 ) , ( − 2 , 1 , − 1 ) and ( 1 , 2 , 5 ) Such that basis over the respective coordinates will be A = [ 1 1 2 ] B = [ 2 3 9 ] C = [ − 2 1 − 1 ] D = [ 1 2 5 ] Vector displacement over the basis vectors A B → = [ 2 3 9 ] − [ 1 1 2 ] = [ 1 2 7 ] A C → = [ − 2 1 − 1 ] − [ 1 1 2 ] = [ − 3 0 − 3 ] A D → = [ 1 2 5 ] − [

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

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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 …

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Chapter 2.SE, Problem 11SE

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Determine whether the four points (1,1,2),(2,3,9),(−2,1,−1) and (1,2,5) lies on the same plane.

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Chapter 2.SE, Problem 10SE

Chapter 2.SE, Problem 12SE

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Chapter 2 Solutions

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 2.1 - In Exercises 1-4, graph the geometric vector u=AB...Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Let u=AB and v=CD where...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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Determine whether the four points ( 1 , 1 , 2 ) , ( 2 , 3 , 9 ) , ( − 2 , 1 , − 1 ) and ( 1 , 2 , 5 ) lies on the same plane.

Solution Summary: The author explains how to determine whether the four points in the field lie on the same plane.

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Determine whether the four points (1,1,2),(2,3,9),(−2,1,−1) and (1,2,5) lies on the same plane.

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