The vectors v1, v2 and v3 form an orthonormal basis for R3 where v1:=vector([0,0,-1]); v2:=vector([1/sqrt(2),1/sqrt(2),0]); v3:=vector([-1/sqrt(2),1/sqrt(2),0]); The coordinates of the vector w:=vector([1,-1,1]) with respect to the basis vectors v1, v2 and v3 of R3 are

The vectors v1, v2 and v3 form an orthonormal basis for R3 where v1:=vector([0,0,-1]); v2:=vector([1/sqrt(2),1/sqrt(2),0]); v3:=vector([-1/sqrt(2),1/sqrt(2),0]); The coordinates of the vector w:=vector([1,-1,1]) with respect to the basis vectors v1, v2 and v3 of R3 are

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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Question

The vectors v1, v2 and v3 form an orthonormal basis for R3 where
v1:=vector([0,0,-1]);
v2:=vector([1/sqrt(2),1/sqrt(2),0]);
v3:=vector([-1/sqrt(2),1/sqrt(2),0]);
The coordinates of the vector w:=vector([1,-1,1]) with respect to the basis vectors v1, v2 and v3 of R3 are:

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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