Answered: Problem 5. (a) Prove that the vectors… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 19E

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Problem 5. (a) Prove that the vectors
V₁ =
V2 =
and v3
=
0
form an orthogonal basis of R³ with the usual dot product.
(b) Use orthogonality to write the vector v = (1,2,3) as a linear combination of V1, V2, V3.
(c) Construct an orthonormal basis from the given vectors.
(d) Write vas a linear combination of the vectors in the orthonormal basis you found in (c).

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