According to Jenann Ismael, Quantum Mechanics is a mathematical machine for predicting the behaviors of microscopic particles. In relation to vectors, Quantum Mechanics deals with Hilbert space, a vector space with an inner product defined. An example of this finite hilbert spaces are real numbers and complex numbers. Quantum mechanics may sound seem too complex, and it is, but it’s practical uses are for building precise clocks, creating super computers, imporivng microscopes, and formulating uncrackable codes.

Ismael, Jenann. “Quantum Mechanics.” From Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/qm/#QuaMec

Weisstein, Eric W. “Hilbert Space.” From MathWorld–A Wolfram Web Resource.

Jenner, Nicola. “Five Practical Uses for ‘Spooky’ Quantum Mechanics.” From
Smithsonian.com http://www.smithsonianmag.com/science-nature/five-practical-uses-spooky-quantum-mechanics-180953494/