What would happen if we ran out of some rare metals used in technology?

Explanation:

Extracting the rare earth elements used in "green" tech is flagrantly dirty. Radioactive minerals such as uranium and thorium are concentrated in the waste rock and sludge produced during mining. Then processing the rare earth minerals causes more severe damage to the land [source: EPA].

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west