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1) Given is a vector A. In Cartesian coordinates it is given by A = x + 2y + 32 (0.1) Now we introduce a second (orthonormal, right-handed as usual) coordi- nate system with basis vectors â = :X + b = 2 Ĉ = ? a) Find the a,b, and c-components of A, i.e. (0.2) (0.3) (0.4) A = A₂â+A₂b + Acc (0.5) b) Check that the length of the vector A = VAA ism the same, no matter if the dot product is evaluated in the x,y,z or a,b,c coordinate system.

1) Given is a vector A. In Cartesian coordinates it is given by A = x + 2y + 32 (0.1) Now we introduce a second (orthonormal, right-handed as usual) coordi- nate system with basis vectors â = :X + b = 2 Ĉ = ? a) Find the a,b, and c-components of A, i.e. (0.2) (0.3) (0.4) A = A₂â+A₂b + Acc (0.5) b) Check that the length of the vector A = VAA ism the same, no matter if the dot product is evaluated in the x,y,z or a,b,c coordinate system.

Advanced Engineering Mathematics
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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1) Given is a vector A. In Cartesian coordinates it is given by (0.1) Now we introduce a second (orthonormal, right-handed as usual) coordi- nate system with basis vectors A = x + 2y + 32 √₂x b Ź Ĉ = ? A = 1 a) Find the a,b, and c-components of A, i.e. A â + A₂b + Acc (0.2) (0.3) (0.4) (0.5) = b) Check that the length of the vector A VAA ism the same, no matter if the dot product is evaluated in the x,y,z or a,b,c coordinate system.
Transcribed Image Text:1) Given is a vector A. In Cartesian coordinates it is given by (0.1) Now we introduce a second (orthonormal, right-handed as usual) coordi- nate system with basis vectors A = x + 2y + 32 √₂x b Ź Ĉ = ? A = 1 a) Find the a,b, and c-components of A, i.e. A â + A₂b + Acc (0.2) (0.3) (0.4) (0.5) = b) Check that the length of the vector A VAA ism the same, no matter if the dot product is evaluated in the x,y,z or a,b,c coordinate system.
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