Consider the following vectors in R³: (0) V₁ √3 4 V₂ = 72 = √6 1 (a) Show that these vectors are orthonormal. (b) Explain why it is then clear that 7₁, 72, V3 is a basis for R³. (c) Compute the coordinates for the following vectors in the basis 7₁, V2, V3: -3 uz 2 In each case, confirm your solution. 1:52 = V3 - (9). () 0 0 7 (-) 2

Consider the following vectors in R³: (0) V₁ √3 4 V₂ = 72 = √6 1 (a) Show that these vectors are orthonormal. (b) Explain why it is then clear that 7₁, 72, V3 is a basis for R³. (c) Compute the coordinates for the following vectors in the basis 7₁, V2, V3: -3 uz 2 In each case, confirm your solution. 1:52 = V3 - (9). () 0 0 7 (-) 2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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