Are the planes given by Π1 : 2x − 3y + z − 1 = 0 and Π2 : 3x − 2y + 4z − 7 = 0 parallel? Justify your answer. (That means you must provide a proof of your claim.) (b) If Π1 and Π2 are not parallel, then Π1 and Π2 intersect along a line ℓ . Does ℓ intersect the xy-plane? Justify your answer. (That means you must provide a proof of your claim.)

Are the planes given by Π1 : 2x − 3y + z − 1 = 0 and Π2 : 3x − 2y + 4z − 7 = 0 parallel? Justify your answer. (That means you must provide a proof of your claim.) (b) If Π1 and Π2 are not parallel, then Π1 and Π2 intersect along a line ℓ . Does ℓ intersect the xy-plane? Justify your answer. (That means you must provide a proof of your claim.)

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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