Problem:
Orthogonalize the following vectors:
${\{-1,-2,-3\}, \{-3,-2,-3\}, \{-1,-2,-3\}}$
Answer:
${\left\{-\frac{1}{\sqrt{14}},-\sqrt{\frac{2}{7}},-\frac{3}{\sqrt{14}}\right\}, \left\{-\sqrt{\frac{13}{14}},\sqrt{\frac{2}{91}},\frac{3}{\sqrt{182}}\right\}, \{0,0,0\}}$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/orthogonalize_vectors/37233.txt'}