(a) Is there a plane containing the the point P(2, −1, 3) and the line ℓ given by ℓ : ⟨x, y, z⟩ = ⟨2 − t, 3 − 2t, −3t⟩, for some parameter t? Justify your answer. (b) If there is a plane containing ℓ and P, then find the equation of the plane. Simplify your answer.

(a) Is there a plane containing the the point P(2, −1, 3) and the line ℓ given by ℓ : ⟨x, y, z⟩ = ⟨2 − t, 3 − 2t, −3t⟩, for some parameter t? Justify your answer. (b) If there is a plane containing ℓ and P, then find the equation of the plane. Simplify your answer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 13AEXP

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Question

(a) Is there a plane containing the the point P(2, −1, 3) and the line ℓ given by
ℓ : ⟨x, y, z⟩ = ⟨2 − t, 3 − 2t, −3t⟩, for some parameter t? Justify your answer.
(b) If there is a plane containing ℓ and P, then find the equation of the plane.
Simplify your answer.

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