1. Show that the vectors(1/(3√2), 1/(3√√2), -4/(3√√/2)), (2/3,2/3, 1/3), (1/√√2, -1/√√2,0)form an orthonormal basis of R³. Find the coordinates of the vector(1, 4, 3) with respect to that basis.

To show that the given vectors form an orthonormal basis of ℝ³, we need to verify two conditions:…

Answered: 1. Show that the vectors (1/(3√2),…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Answer no. 3 only please

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1. Show that the vectors (1/(3√2), 1/(3√√2), –4/(3√√2))¹, (2/3,2/3,1/3), (1/√√2, -1/√√2,0)¹ form an orthonormal basis of R³. Find the coordinates of the vector (1, 4, 3) with respect to that basis.