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Mathematics-Online problems:

Interactive Problem 172, Version 1: Orthogonal Basis, Coefficients with respect to an Orthogonal Basis

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[Version 1] [next]
version   
Find the missing components of $ \vec{c}$, such that each pair of the vectors

$ \vec{a}= \left(\rule{0pt}{8ex}\right.$
1
0
1
$ \left.\rule{0pt}{8ex}\right)$ , $ \vec{b} = \left(\rule{0pt}{8ex}\right.$
-1
2
1
$ \left.\rule{0pt}{8ex}\right)$ , $ \vec{c}= \left(\rule{0pt}{8ex}\right.$
1
$ \left.\rule{0pt}{8ex}\right)$ .

are orthogonal. Determine $ \alpha,\beta,\gamma\in \mathbb{R}$ such that

$\displaystyle \left(\begin{array}{c} 5 \\ 2 \\ 1 \end{array}\right) = \alpha\,\vec{a} + \beta\,\vec{b} + \gamma\,\vec{c} \; . $

$ \alpha \ =$ ,         $ \beta \ =$ ,          $ \gamma \ =$ .


  

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  automatically generated: 8/11/2017